Nonlinear Dynamics and Complex Systems
学科专业代码（Subjectcode）
学科专业代码（Subject code）Information worth havingIt comes from the accumulation of learningThere must be a problemAlso please criticize the correct!The total number of students in 2012 is 150Includes the following major:Subject code070200Subject namephysicsEnter oneself for an examination conditionsBachelor degree in physics and similar disciplinesMajor contents include:The department of physics of the university of science and technology of China is a first-degree subject in the stateIt is the basic science research and teaching talent trainingbase of national scienceThe physics experimental teaching center is the first national model teaching center of the countryThe first level of physics relies on hefei micro-scale material science national laboratory to carry out scientific researchAnd has built "nuclear detection technology and the national key laboratory of nuclear power.""Key laboratory of quantum information of Chinese academy of sciences" and "key laboratory of basic plasma of Chinese academy of sciences" and key laboratory of optoelectronic science and technology in anhui provinceThe first class of physics is aimed at cultivating the leading talents in the basic research, applied research and development of the frontier and cross sciencePay attention to the students' physical quality and innovative spirit cultivationOver the years,A large number of outstanding talents have been cultivated in different fieldsIncluding 10 academicians of Chinese academy of sciences and Chinese academy of engineeringA number of generals engaged in national defenseAs well as young scholars active in the forefront of international scientific research, nine of the doctoral graduates have won the national 100 excellent doctoral dissertation awardPhysics first-level disciplines have a physics postdoctoral stationAnd won the title of outstanding postdoctoral research station in 2010The first level of physics covers six secondary disciplinesTheoretical physics, particle physics and nuclear physics, atomic molecular physics, plasma physics, condensed matter physics, optics1) theoretical physics research directions: 1. Superstring/M theory, gravity and polar early cosmology; 2. Quantum field theory, elementary particle theory and its phenomenology; 3. Statistical physics, nonlinear dynamics and complex system theory; 4. Condensed matter theory, quantum mechanics principle and application2) the research directions of particle physics and nuclear physics are: 1. High energy particle physicsStudy on the theory of particle physics and experimental analysis, new detector and new exploration technology; 2.Nuclear spectroscopy and nuclear technologyCovering the application of nuclear technology in materials, chemistry, industry, biology and medicine; Quantum communication and quantum computing3) the research directions of atomic molecular physics include: 1. Electron collision spectroscopy; 2. Quantum information and quantum physics; 3. Atomic recognition and measurement and control; 4. Synchronous radiation spectroscopy4) the research directions of plasma physics include: 1. Magnetic confinement fusion plasma physics; 2. Inertial confinement fusion plasma physics; Low temperature plasma and its high technology applications; 4. Basic plasma physics5) the research direction of condensed matter physics is: 1.2. Advanced functional materials and physics;3. Nanostructures and single molecular science;4. Theory and calculation of electronic structure.6) optical research direction: 1. Quantum information and quantum optics; 2. Photonics and technology and biophoton technologyThe exam subject is general physicsThe course II examination subject is quantum mechanics. (among them, the class II examination subject for the physics of plasma physics is electrodynamics)The main direction of graduate school of physics isMost go on to study at home and abroadPart to the research unit and the three capital enterprise work Master's research directionMaster's test subjectscoveragebibliography1-1. Superstring/M theory, gravity and polar early cosmology1-2. Quantum field theory, elementary particle theory and its phenomenology1-3. Statistical physics, nonlinear dynamics and complex systems theory1-4. Condensed matter theory, quantum mechanics principle and application2-1. High energy particle physics, which covers the theoretical and experimental analysis of particle physics, new detectors and new exploration technologies;2-2. Nuclear spectroscopy and nuclear technologyCovering the application of nuclear technology in materials, chemistry, industry, biology and medicine;2-3. Quantum communication and quantum computing4-1. Magnetic confinement fusion plasma physics4-2. Inertial confinement fusion plasma physics4-3. Low temperature plasma and its high technical application4-4. Basic plasma physics5-1. Electronic strong correlation materials and physics5-2. Advanced functional materials and physics5-3. Nanostructures and single-molecule science5-4. Electronic structure theory and calculation6-1. Quantum information and quantum optics6-2. Photonics and technology and biophoton technology1.101 political theory2.201 English one3.617 ordinary physics A4.828 quantum mechanics (807 electrodynamics A) ** electrodynamics is limited to candidates for plasma physics majors1. General physics: including mechanics, electromagnetism.2Quantum mechanics, including the concept of atomic physics, quantum mechanics and the basic principle, the wave function and wave equation, the problem of one dimensional steady state, symmetry and conservation law of mechanical quantity operator, central field, particle movement in the electromagnetic field, spin, stationary state perturbation theory, the quantum leap3. Electrodynamics:1. Physical textbooks of physics department of China university of science and technology, Peking University or other universities2. The first volume of quantum mechanics, zeng jinScience pressThe form and content of the retrialBecause students are enrolled in the first classIn the first test, the exam is relatively broadMore specialized courses will be reviewed in the second interviewSubject code070400Subject nameastronomyEnter oneself for an examination conditionsPhysics and astronomy university graduate studentMajor contents include:The university of science and technology of science and technology is the first batch of senior personnel training base, including undergraduate, master degree, doctoral degree and post-doctoral research stationIn 1986, he received the right to grant an astrophysics doctorate and master's degreeIn 1999, it was assessed by the ministry of education as a national key subjectIn 2008, the ministry of education assessed the national science talent cultivation baseThe key laboratory of science galaxy cosmology was jointly constructed by the Shanghai observatory in 2008Astronomy majors now include a second level subject in astrophysicscosmologyGalaxies and active galaxies, high energy and relativistic astrophysics, astronomical technology, solar system, and other research directionsThe major employment orientation of this major is the astronomical research and education talents of the observatory and universitiesMaster's research directionMaster's test subjectscoveragebibliographyGalactic cosmologyHigh energy relativistic astrophysicsAstronomical technologyexoplanet1.101 political theory2.201 English one3.617 ordinary physics A4.807 electrodynamics AThe form and content of the retrialMathematical synthesis and physical comprehensive written examination and oral examinationSubject code080300Subject nameOptical engineeringEnter oneself for an examination conditionsIndicate which kinds of students to recruit studentsMajor contents include:Our school of optics engineeringThe existing majors include quantum cryptography, optoelectronic technology, environmental optics, short-wave optics and modern displayIts research platform for the Chinese academy of sciences key laboratory of quantum information, key laboratory of optoelectronic science and technology of anhui province and hefei two provincial key laboratory of modern display research institute as the main supportThe subject of quantum cryptography is the first team to conduct this research in ChinaThere is a certain amount of influence in the worldIt is the most important research base of quantum information in ChinaAn innovative team of young PHDS has been establishedThree consecutive years of inclusion in the fund committee outstanding innovation groupI was selected as the international partner program of cas knowledge innovation teamThe field of optoelectronic technology is mainly engaged in the research of fiber laser and amplification technology, optical sensing, nano photon technology, optical tweezers technology and polymer photon technologyIt is one of the earliest research institutes on the technology of functional polymer fiber, polymer fiber amplifier and optical tweezersThe direction of environmental optics enjoys a high academic reputation both at home and abroadIt is the key base of environmental monitoring of Chinese academy of sciencesThe spectral diagnosis and application of short wave optical technology in the direction of synchronous radiation, strong laser, X-ray laser and laser plasma light sourceIt is the sole unit of the large aperture grating that can provide strong laser at homeModern display technology is mainly engaged in liquid crystal display and laser display of key technical problemsIt is supported by anhui photoelectron science and technology key laboratory and hefei modern display research instituteAcademician ouyang zhong can be the leader of the main subject in this directionThe field of employment of graduates of this subject mainly includes: research institutes, large and medium-sizedhigh-tech companies, and overseas studyMaster's research directionMaster's test subjectscoveragebibliographyQuantum cryptographyOptoelectronic technologyModern display technologyOptical environmentShort-wave opticsThe political theory(2) a 201 English(3) 301 a mathematicsEngineering opticsThe form and content of the retrialWritten test and interviewThe written test is mainly about quantum information, laser technology and optoelectronic technologySubject code080900Subject nameElectronic science and technologyEnter oneself for an examination conditionsUniversity graduate with bachelor's degreeMajor contents include:Electronic science and technology level subject covers: physical electronics (080901), circuits and systems (080902), microelectronics and solid-state electronics (080903), and the electromagnetic field and microwave technology (080904) 4 secondary professional disciplinesThe main research directions for each secondary subject are as follows:Physical electronicsPhysical electronics is the interdisciplinary subject of modern physics, electronics, optoelectronics, quantum electronics, nanoelectronics and related technologiesBasic and applied research in the field of electronic scienceengineering and information science and technologyThis subject is mainly aimed at the demand of high-level talents for the development of the state in the field of physics and electronicsCultivate understanding of the frontier and dynamics of this disciplineHave high professional level, strong analysis and problem solving ability, can adapt to various complex environment, can independently engage in research and development work of high level research talentThis subject is affiliated to nuclear exploration and nuclear nuclear research state key laboratoryMain research directions:1. High accuracy and large dynamic range charge measurement method2. Measurement method of the time interval of picosecond accuracy3. High speed waveform digitization and large capacity data acquisition technology4. Quantum communication technology5. X-ray correlation imaging6. Special nuclear information processing IC ASIC design and applicationEnrollment number: 25Expected number of recipients: 10Microelectronics and solid electronicsMicroelectronics and solid-state electronics have enjoyed a high reputation in China with high frequency signal processing, analog integrated circuit design and electric power automation system designThis discipline is dedicated to the construction of this academic field into new functional materials, new device physics and integrated circuits (especially ASIC) in various environmentsThe design and application of the integrated system are studiedDeveloped microelectronic professionalsMainly to related universities, research institutes andwell-known international high-tech enterprisesAnd further study abroadThe employment situation is very goodMain research directions:1. Physical research of semiconductor devicesA study of semiconductor devices based on new materials and structures2. Design and application of power electronics devices; Computer simulation of semiconductor device model3. Research on integrated circuit design methodIn particular, special integrated circuit design and testing techniques are applied in aerospace, military and communication fields4. Research on computer aided design technology, SOC design and applicationEnrollment number: 8Expected number of recipients: 3Master's research directionMaster's test subjectscoveragebibliographyPhysical electronics01 data acquisition and signal processing02 fast electronics03 X-ray correlation imagingQuantum communication technologyThe political theory(2), 201 English(3) 301 a mathematics810 electronics foundationBasis of circuit analysisElectronic technology foundationPrinciple of microcomputerLi han-sun, the foundation of circuit analysis Higher education press;"Electronic technology foundation" kang hua guang Higher education press;"Microcomputer principle and interface technology" wu xiuqingChina science and technology university pressMicroelectronics and solid electronics01 semiconductor deviceDevice physics and device modelSpecial integrated circuit design and application03 power electronics devices and applicationsSystem integrated chip SOC design and applicationPolitical theory(2) a 301 English(3) 301 a mathematics801 semiconductor integrated circuitThe principle, structure, design and application of digital integrated circuitTo simulate the principle, structure, design and application of integrated circuit1. Digital integrated circuit design perspective2. Principle, design and application of analog integrated circuitThe form and content of the retrialThe interview is combined with written test and interview: the written test is ordinary physicsInterviews with three professors or associate professors interview candidatesIt mainly investigates the students' background knowledge, analysis and problem-solving ability。
Robust Control and Estimation
Robust Control and Estimation Robust control and estimation are essential concepts in the field of engineering, particularly in the realm of system dynamics and feedback control. These techniques play a crucial role in ensuring the stability and performance of complex systems in the presence of uncertainties and disturbances. Robust control refers to the design of control systems that can effectively handle variations in system parameters and external disturbances, while robust estimation involves the development of algorithms to accurately estimate the state of a system despite uncertainties in the measurements. One of the key challenges in robust control and estimation is dealing with uncertainties in the system model. In many real-world applications, the exact dynamics of the system may not be known with certainty, leading to the need for robust control and estimation techniques that can accommodate these uncertainties. Robust control methods such as H-infinity control and mu-synthesis provide a systematic framework for designing controllers that can guarantee stability and performance in the presence of uncertainties. Another important aspect of robust control and estimation is the consideration of disturbances and noise in the system. These external factors can significantly impact the performance of a control system, leading to instability or degraded performance if not properly accounted for. Robust control and estimation techniques aim to mitigate the effects of disturbances and noise by designing controllers and estimators that are resilient to these external factors. In addition to uncertainties and disturbances, robust control and estimation also play a crucial role in ensuring the safety and reliability of critical systems. In applications such as aerospace, automotive, and industrial control, robust control techniques are essential for guaranteeing the stability and performance of the system under various operating conditions. By incorporating robust control and estimation methods, engineers can design systems that are more resilient to uncertainties and disturbances, ultimately enhancing the safety and reliability of the overall system. Moreover, robust control and estimation techniques are also essential for addressing the challenges posed by nonlinear and time-varying systems. Traditional control methods may struggle to handle the complexities introduced by nonlinear dynamics and time-varying parameters, making robustcontrol and estimation techniques indispensable in such scenarios. By leveraging robust control methods such as adaptive control and nonlinear control, engineers can effectively address the challenges posed by nonlinear and time-varying systems, ensuring stable and reliable performance in the face of changing dynamics. In conclusion, robust control and estimation are vital tools in the field of engineering, enabling the design of control systems that can effectively handle uncertainties, disturbances, and nonlinearities. By incorporating robust control and estimation techniques, engineers can enhance the stability, performance, and reliability of complex systems, ultimately contributing to the advancement of technology and innovation. As the complexity of engineering systems continues to grow, the importance of robust control and estimation will only increase, underscoring the need for continued research and development in this critical area.。
杜克物理
ResearchAccelerator PhysicsTom Katsouleas: use of plasmas as novel particle accelerators and light sources Ying Wu: nonlinear dynamics of charged particle beams, coherent radiation sources, and the development of novel accelerators and light sourcesBiological PhysicsNick Buchler: Molecular mechanisms and the evolution of switches and oscillators in gene networks; systems biology; comparative genomicsGlenn Edwards: Interests include 1) the transduction of light to vibrations to heat and pressure in biological systems and 2) how biology harnesses physical mechanisms during pattern formation in early Drosophila development.Gleb Finkelstein: Electronic transport in carbon nanotubes and graphene; Inorganic nanostructures based on self-assembled DNA scaffolds.Henry Greenside: Theoretical neurobiology in collaboration with Dr. Richard Mooney's experimental group on birdsong.Calvin Howell: Measurement of the neutron-neutron scattering length, carbon and nitrogen accumulation and translocation in plants.Joshua Socolar: Organization and function of complex dynamical networks, especially biological networks, including electronic circuits and social interaction networksWarren Warren: novel pulsed techniques, using controlled radiation fields to alter dynamics; ultrafast laser spectroscopy or nuclear magnetic resonanceCondensed Matter PhysicsHarold Baranger: Theory of quantum phenomena at the nanometer scale;many-body effects in quantum dots and wires; conduction through single molecules; quantum computing; quantum phase transitionsRobert Behringer: Experiments on instabilities and pattern formation in fluids; flow, jamming, and stress patterns in granular materials.David Beratan: molecular underpinnings of energy harvesting and charge transport in biology; the mechanism of solar energy capture and conversion in man-made structuresShailesh Chandrasekharan: Theoretical studies of quantum phase transitions using quantum Monte Carlo methods; lattice QCDAlbert Chang: Experiments on quantum transport at low temperature;one-dimensional superconductivity; dilute magnetic semiconductor quantum dots; Hall probe scanning.Patrick Charbonneau: in- and out-of-equilibrium dynamical properties ofself-assembly. Important phenomena, such as colloidal microphase formation, protein aggregation.Stefano Curtarolo: Nanoscale/microscale computing systems & Quantum Information.Gleb Finkelstein: Experiments on quantum transport at low temperature; carbon nanotubes; Kondo effect; cryogenic scanning microscopy; self-assembled DNA templates.Jianfeng Lu: Mathematical analysis and algorithm development for problems from computational physics, theoretical chemistry, material sciences and others. Maiken H. Mikkelsen: Experiments in Nanophysics & Condensed Matter Physics Richard Palmer: Theoretical models of learning and memory in neural networks; glassy dynamics in random systems with frustrated interactions.Joshua Socolar: Theory of dynamics of complex networks; Modeling of gene regulatory networks; Structure formation in colloidal systems; Tiling theory and nonperiodic long-range order.David Smith: theory, simulation and characterization of unique electromagnetic structures, including photonic crystals and metamaterialsStephen Teitsworth: Experiments on nonlinear dynamics of currents in semiconductors.Weitao Yang: developing methods for quantum mechanical calculations of large systems and carrying out quantum mechanical simulations of biological systems and nanostructuresHigh Energy PhysicsAyana Arce: Searches for top quarks produced in massive particle decays, Jet substructure observable reconstruction, ATLAS detector simulation software frameworkAlfred T. Goshaw: Study of Nature's most massive particles, the W and Z bosons (carriers of the weak force) and the top quark.Ashutosh Kotwal: Experimental elementary particle physics; instrumentation, Precisely measure the mass of the W boson, which is sensitive to the quant um mechanical effects of new particles or forces.Mark Kruse: Higgs boson, production of vector boson pairs, andmodel-independent analysis techniques for new particle searches.Seog Oh: High mass di-lepton search, WW and WZ resonance search, A SUSY particle search, HEP detector R&DKate Scholberg: Experimental particle physics and particle astrophysics; neutrino physics with beam, atmospheric and supernova neutrinos (Super-K, T2K, LBNE, HALO, SNEWS)Chris Walter: Experimental Particle Physics, Neutrino Physics,Particle-Astrophysics, Unification and CP ViolationImaging and Medical PhysicsJames T. Dobbins III: advanced imaging applications to improve diagnostic accuracy in clinical imaging, scientific assessment of image quality, developing lower cost imaging for the developing worldBastian Driehuy: developing and applying hyperpolarized gases to enable fundamentally new applications in MRIAlan Johnson: engineering physics required to extend the resolution of MR imaging and in a broad range of applications in the basic sciencesEhsan Samei: design and utilization of advanced imaging techniques aimed to achieve optimum interpretive, quantitative, and molecular performanceWarren Warren: novel pulsed techniques, using controlled radiation fields to alter dynamics; ultrafast laser spectroscopy or nuclear magnetic resonanceNonlinear and Complex SystemsThe Center for Nonlinear and Complex Systems (CNCS) is an interdisciplinar y University-wide organization that fosters research and teaching of nonlinear dynamics, chaos, pattern formation and complex nonlinear systems with many degrees of freedom.Robert Behringer: Experiments on instabilities and pattern formation in fluids; flow, jamming, and stress patterns in granular materials.Patrick Charbonneau: in- and out-of-equilibrium dynamical properties ofself-assembly. Important phenomena, such as colloidal microphase formation, protein aggregation.Henry Greenside: Theory and simulations of spatiotemporal patterns in fluids; synchronization and correlations in neuronal activity associated with bird song. Daniel Gauthier: Experiments on networks of chaotic elements; generation and control of high speed chaos in electronic and optical systems; electrodynamics of cardiac tissue and the onset of fibrillation.Jian-Guo Liu: Applied mathematics, nonlinear dynamics, complex system, fluid dynamics, computational sciencesRichard Palmer: Theoretical models of learning and memory in neural networks; glassy dynamics in random systems with frustrated interactions.Joshua Socolar: Theory of dynamics of random networks with applications to gene regulation; stress patterns in granular materials; stabilization of periodic orbits in chaotic systems.Stephen Teitsworth: Experiments on nonlinear dynamics of currents in semiconductors.Ying Wu: nonlinear dynamics of charged particle beams, coherent radiation sources, and the development of novel accelerators and light sourcesTom Katsouleas: use of plasmas as novel particle accelerators and light sourcesExperimental Nuclear PhysicsThe Duke physics department is the host of the Triangle Universities Nuclear Laboratory consisting of three experimental facilities: LENA, FN tandem Van de Graff, and The High Intensity Gamma Source (HIGS) at the Free Electron Laser Laboratory.Mohammad Ahmed: Study of few nucleon systems with hadronic and gamma-ray probes.Phillip Barbeau: Experimental Nuclear & Particle Astro-Physics, Double Beta Decay, Neutrinos and Dark MatterHaiyan Gao: Neutron EDM, Precision measurement of proton charge radius, Polarized Compton scattering, neutron and proton transversity, search for phi-N bound state, polarized photodisintegration of 3HeCalvin Howell: quantum chromodynamics (QCD) description of structure and reactions of few-nucleon systems, Big Bang and explosive nucleosynthesis, and applications of nuclear physics in biology, medicine and national security Werner Tornow: weak-interaction physics, especially in double-beta decay studies and in neutrino oscillation physics using large scale detectors at the Kamland project in Japan.Henry Weller: Using radiative capture reactions induced by polarized beams of protons and deuterons to study nuclear systemsYing Wu: nonlinear dynamics of charged particle beams, coherent radiation sources, and the development of novel accelerators and light sourcesTheoretical Nuclear and Particle PhysicsSteffen A. Bass: Physics of the Quark-Gluon-Plasma (QGP) and ultra-relativistic heavy-ion collisions used to create such a QGP under controlled laboratory conditions.Shailesh Chandrasekharan: Quantum Critical Behavior in Fermion Systems, Using the generalized fermion bag algorithm, Applications to Graphene and Unitary Fermi Gas.Thomas Mehen: Quantum Chromodynamics (QCD) and the application of effective field theory to hadronic physics.Berndt Müller: Nuclear matter at extreme energy density; Quantum chromodynamics.Roxanne P. Springer: Weak interactions (the force responsible for nuclear beta decay) and quantum chromodynamics (QCD, the force that binds quarks into hadrons).Geometry and Theoretical PhysicsPaul Aspinwall: String theory is hoped to provide a theory of all fundamental physics encompassing both quantum mechanics and general relativity.Hubert Bray: geometric analysis with applications to general relativity and the large-scale geometry of spacetimes.Ronen Plesser: String Theory, the most ambitious attempt yet at a comprehensive theo ry of the fundamental structure of the universe.Arlie Petters: problems connected to the interplay of gravity and light (gravitational lensing, general relativity, astrophysics, cosmology)Quantum Optics/Ultra-cold atomsDaniel Gauthier: Topics in the fields of nonlinear and quantum optics, and nonlinear dynamical systems.Jungsang Kim: Quantum Information & Integrated Nanoscale SystemsMaiken H. Mikkelsen: Experiments in Nanophysics & Condensed Matter Physics∙Duke University Department of Physics∙Physics Bldg., Science Dr.∙Box 90305∙Durham, NC 27708∙Phone: 919-660-2500∙Fax: 919-660-2525NetID LoginE-Newsletter Sign UpSign up to receive a monthly E-Newsletter or an Annual print Newsletter and keep up with the Physics Department’s scholarly activities∙∙∙∙∙DUKE UNIVERSITY∙GIVING @ DUKE∙WORKING ENVIRONMENT POLICY。
人工智能领域中英文专有名词汇总
名词解释中英文对比<using_information_sources> social networks 社会网络abductive reasoning 溯因推理action recognition(行为识别)active learning(主动学习)adaptive systems 自适应系统adverse drugs reactions(药物不良反应)algorithm design and analysis(算法设计与分析) algorithm(算法)artificial intelligence 人工智能association rule(关联规则)attribute value taxonomy 属性分类规范automomous agent 自动代理automomous systems 自动系统background knowledge 背景知识bayes methods(贝叶斯方法)bayesian inference(贝叶斯推断)bayesian methods(bayes 方法)belief propagation(置信传播)better understanding 内涵理解big data 大数据big data(大数据)biological network(生物网络)biological sciences(生物科学)biomedical domain 生物医学领域biomedical research(生物医学研究)biomedical text(生物医学文本)boltzmann machine(玻尔兹曼机)bootstrapping method 拔靴法case based reasoning 实例推理causual models 因果模型citation matching (引文匹配)classification (分类)classification algorithms(分类算法)clistering algorithms 聚类算法cloud computing(云计算)cluster-based retrieval (聚类检索)clustering (聚类)clustering algorithms(聚类算法)clustering 聚类cognitive science 认知科学collaborative filtering (协同过滤)collaborative filtering(协同过滤)collabrative ontology development 联合本体开发collabrative ontology engineering 联合本体工程commonsense knowledge 常识communication networks(通讯网络)community detection(社区发现)complex data(复杂数据)complex dynamical networks(复杂动态网络)complex network(复杂网络)complex network(复杂网络)computational biology 计算生物学computational biology(计算生物学)computational complexity(计算复杂性) computational intelligence 智能计算computational modeling(计算模型)computer animation(计算机动画)computer networks(计算机网络)computer science 计算机科学concept clustering 概念聚类concept formation 概念形成concept learning 概念学习concept map 概念图concept model 概念模型concept modelling 概念模型conceptual model 概念模型conditional random field(条件随机场模型) conjunctive quries 合取查询constrained least squares (约束最小二乘) convex programming(凸规划)convolutional neural networks(卷积神经网络) customer relationship management(客户关系管理) data analysis(数据分析)data analysis(数据分析)data center(数据中心)data clustering (数据聚类)data compression(数据压缩)data envelopment analysis (数据包络分析)data fusion 数据融合data generation(数据生成)data handling(数据处理)data hierarchy (数据层次)data integration(数据整合)data integrity 数据完整性data intensive computing(数据密集型计算)data management 数据管理data management(数据管理)data management(数据管理)data miningdata mining 数据挖掘data model 数据模型data models(数据模型)data partitioning 数据划分data point(数据点)data privacy(数据隐私)data security(数据安全)data stream(数据流)data streams(数据流)data structure( 数据结构)data structure(数据结构)data visualisation(数据可视化)data visualization 数据可视化data visualization(数据可视化)data warehouse(数据仓库)data warehouses(数据仓库)data warehousing(数据仓库)database management systems(数据库管理系统)database management(数据库管理)date interlinking 日期互联date linking 日期链接Decision analysis(决策分析)decision maker 决策者decision making (决策)decision models 决策模型decision models 决策模型decision rule 决策规则decision support system 决策支持系统decision support systems (决策支持系统) decision tree(决策树)decission tree 决策树deep belief network(深度信念网络)deep learning(深度学习)defult reasoning 默认推理density estimation(密度估计)design methodology 设计方法论dimension reduction(降维) dimensionality reduction(降维)directed graph(有向图)disaster management 灾害管理disastrous event(灾难性事件)discovery(知识发现)dissimilarity (相异性)distributed databases 分布式数据库distributed databases(分布式数据库) distributed query 分布式查询document clustering (文档聚类)domain experts 领域专家domain knowledge 领域知识domain specific language 领域专用语言dynamic databases(动态数据库)dynamic logic 动态逻辑dynamic network(动态网络)dynamic system(动态系统)earth mover's distance(EMD 距离) education 教育efficient algorithm(有效算法)electric commerce 电子商务electronic health records(电子健康档案) entity disambiguation 实体消歧entity recognition 实体识别entity recognition(实体识别)entity resolution 实体解析event detection 事件检测event detection(事件检测)event extraction 事件抽取event identificaton 事件识别exhaustive indexing 完整索引expert system 专家系统expert systems(专家系统)explanation based learning 解释学习factor graph(因子图)feature extraction 特征提取feature extraction(特征提取)feature extraction(特征提取)feature selection (特征选择)feature selection 特征选择feature selection(特征选择)feature space 特征空间first order logic 一阶逻辑formal logic 形式逻辑formal meaning prepresentation 形式意义表示formal semantics 形式语义formal specification 形式描述frame based system 框为本的系统frequent itemsets(频繁项目集)frequent pattern(频繁模式)fuzzy clustering (模糊聚类)fuzzy clustering (模糊聚类)fuzzy clustering (模糊聚类)fuzzy data mining(模糊数据挖掘)fuzzy logic 模糊逻辑fuzzy set theory(模糊集合论)fuzzy set(模糊集)fuzzy sets 模糊集合fuzzy systems 模糊系统gaussian processes(高斯过程)gene expression data 基因表达数据gene expression(基因表达)generative model(生成模型)generative model(生成模型)genetic algorithm 遗传算法genome wide association study(全基因组关联分析) graph classification(图分类)graph classification(图分类)graph clustering(图聚类)graph data(图数据)graph data(图形数据)graph database 图数据库graph database(图数据库)graph mining(图挖掘)graph mining(图挖掘)graph partitioning 图划分graph query 图查询graph structure(图结构)graph theory(图论)graph theory(图论)graph theory(图论)graph theroy 图论graph visualization(图形可视化)graphical user interface 图形用户界面graphical user interfaces(图形用户界面)health care 卫生保健health care(卫生保健)heterogeneous data source 异构数据源heterogeneous data(异构数据)heterogeneous database 异构数据库heterogeneous information network(异构信息网络) heterogeneous network(异构网络)heterogenous ontology 异构本体heuristic rule 启发式规则hidden markov model(隐马尔可夫模型)hidden markov model(隐马尔可夫模型)hidden markov models(隐马尔可夫模型) hierarchical clustering (层次聚类) homogeneous network(同构网络)human centered computing 人机交互技术human computer interaction 人机交互human interaction 人机交互human robot interaction 人机交互image classification(图像分类)image clustering (图像聚类)image mining( 图像挖掘)image reconstruction(图像重建)image retrieval (图像检索)image segmentation(图像分割)inconsistent ontology 本体不一致incremental learning(增量学习)inductive learning (归纳学习)inference mechanisms 推理机制inference mechanisms(推理机制)inference rule 推理规则information cascades(信息追随)information diffusion(信息扩散)information extraction 信息提取information filtering(信息过滤)information filtering(信息过滤)information integration(信息集成)information network analysis(信息网络分析) information network mining(信息网络挖掘) information network(信息网络)information processing 信息处理information processing 信息处理information resource management (信息资源管理) information retrieval models(信息检索模型) information retrieval 信息检索information retrieval(信息检索)information retrieval(信息检索)information science 情报科学information sources 信息源information system( 信息系统)information system(信息系统)information technology(信息技术)information visualization(信息可视化)instance matching 实例匹配intelligent assistant 智能辅助intelligent systems 智能系统interaction network(交互网络)interactive visualization(交互式可视化)kernel function(核函数)kernel operator (核算子)keyword search(关键字检索)knowledege reuse 知识再利用knowledgeknowledgeknowledge acquisitionknowledge base 知识库knowledge based system 知识系统knowledge building 知识建构knowledge capture 知识获取knowledge construction 知识建构knowledge discovery(知识发现)knowledge extraction 知识提取knowledge fusion 知识融合knowledge integrationknowledge management systems 知识管理系统knowledge management 知识管理knowledge management(知识管理)knowledge model 知识模型knowledge reasoningknowledge representationknowledge representation(知识表达) knowledge sharing 知识共享knowledge storageknowledge technology 知识技术knowledge verification 知识验证language model(语言模型)language modeling approach(语言模型方法) large graph(大图)large graph(大图)learning(无监督学习)life science 生命科学linear programming(线性规划)link analysis (链接分析)link prediction(链接预测)link prediction(链接预测)link prediction(链接预测)linked data(关联数据)location based service(基于位置的服务) loclation based services(基于位置的服务) logic programming 逻辑编程logical implication 逻辑蕴涵logistic regression(logistic 回归)machine learning 机器学习machine translation(机器翻译)management system(管理系统)management( 知识管理)manifold learning(流形学习)markov chains 马尔可夫链markov processes(马尔可夫过程)matching function 匹配函数matrix decomposition(矩阵分解)matrix decomposition(矩阵分解)maximum likelihood estimation(最大似然估计)medical research(医学研究)mixture of gaussians(混合高斯模型)mobile computing(移动计算)multi agnet systems 多智能体系统multiagent systems 多智能体系统multimedia 多媒体natural language processing 自然语言处理natural language processing(自然语言处理) nearest neighbor (近邻)network analysis( 网络分析)network analysis(网络分析)network analysis(网络分析)network formation(组网)network structure(网络结构)network theory(网络理论)network topology(网络拓扑)network visualization(网络可视化)neural network(神经网络)neural networks (神经网络)neural networks(神经网络)nonlinear dynamics(非线性动力学)nonmonotonic reasoning 非单调推理nonnegative matrix factorization (非负矩阵分解) nonnegative matrix factorization(非负矩阵分解) object detection(目标检测)object oriented 面向对象object recognition(目标识别)object recognition(目标识别)online community(网络社区)online social network(在线社交网络)online social networks(在线社交网络)ontology alignment 本体映射ontology development 本体开发ontology engineering 本体工程ontology evolution 本体演化ontology extraction 本体抽取ontology interoperablity 互用性本体ontology language 本体语言ontology mapping 本体映射ontology matching 本体匹配ontology versioning 本体版本ontology 本体论open government data 政府公开数据opinion analysis(舆情分析)opinion mining(意见挖掘)opinion mining(意见挖掘)outlier detection(孤立点检测)parallel processing(并行处理)patient care(病人医疗护理)pattern classification(模式分类)pattern matching(模式匹配)pattern mining(模式挖掘)pattern recognition 模式识别pattern recognition(模式识别)pattern recognition(模式识别)personal data(个人数据)prediction algorithms(预测算法)predictive model 预测模型predictive models(预测模型)privacy preservation(隐私保护)probabilistic logic(概率逻辑)probabilistic logic(概率逻辑)probabilistic model(概率模型)probabilistic model(概率模型)probability distribution(概率分布)probability distribution(概率分布)project management(项目管理)pruning technique(修剪技术)quality management 质量管理query expansion(查询扩展)query language 查询语言query language(查询语言)query processing(查询处理)query rewrite 查询重写question answering system 问答系统random forest(随机森林)random graph(随机图)random processes(随机过程)random walk(随机游走)range query(范围查询)RDF database 资源描述框架数据库RDF query 资源描述框架查询RDF repository 资源描述框架存储库RDF storge 资源描述框架存储real time(实时)recommender system(推荐系统)recommender system(推荐系统)recommender systems 推荐系统recommender systems(推荐系统)record linkage 记录链接recurrent neural network(递归神经网络) regression(回归)reinforcement learning 强化学习reinforcement learning(强化学习)relation extraction 关系抽取relational database 关系数据库relational learning 关系学习relevance feedback (相关反馈)resource description framework 资源描述框架restricted boltzmann machines(受限玻尔兹曼机) retrieval models(检索模型)rough set theroy 粗糙集理论rough set 粗糙集rule based system 基于规则系统rule based 基于规则rule induction (规则归纳)rule learning (规则学习)rule learning 规则学习schema mapping 模式映射schema matching 模式匹配scientific domain 科学域search problems(搜索问题)semantic (web) technology 语义技术semantic analysis 语义分析semantic annotation 语义标注semantic computing 语义计算semantic integration 语义集成semantic interpretation 语义解释semantic model 语义模型semantic network 语义网络semantic relatedness 语义相关性semantic relation learning 语义关系学习semantic search 语义检索semantic similarity 语义相似度semantic similarity(语义相似度)semantic web rule language 语义网规则语言semantic web 语义网semantic web(语义网)semantic workflow 语义工作流semi supervised learning(半监督学习)sensor data(传感器数据)sensor networks(传感器网络)sentiment analysis(情感分析)sentiment analysis(情感分析)sequential pattern(序列模式)service oriented architecture 面向服务的体系结构shortest path(最短路径)similar kernel function(相似核函数)similarity measure(相似性度量)similarity relationship (相似关系)similarity search(相似搜索)similarity(相似性)situation aware 情境感知social behavior(社交行为)social influence(社会影响)social interaction(社交互动)social interaction(社交互动)social learning(社会学习)social life networks(社交生活网络)social machine 社交机器social media(社交媒体)social media(社交媒体)social media(社交媒体)social network analysis 社会网络分析social network analysis(社交网络分析)social network(社交网络)social network(社交网络)social science(社会科学)social tagging system(社交标签系统)social tagging(社交标签)social web(社交网页)sparse coding(稀疏编码)sparse matrices(稀疏矩阵)sparse representation(稀疏表示)spatial database(空间数据库)spatial reasoning 空间推理statistical analysis(统计分析)statistical model 统计模型string matching(串匹配)structural risk minimization (结构风险最小化) structured data 结构化数据subgraph matching 子图匹配subspace clustering(子空间聚类)supervised learning( 有support vector machine 支持向量机support vector machines(支持向量机)system dynamics(系统动力学)tag recommendation(标签推荐)taxonmy induction 感应规范temporal logic 时态逻辑temporal reasoning 时序推理text analysis(文本分析)text anaylsis 文本分析text classification (文本分类)text data(文本数据)text mining technique(文本挖掘技术)text mining 文本挖掘text mining(文本挖掘)text summarization(文本摘要)thesaurus alignment 同义对齐time frequency analysis(时频分析)time series analysis( 时time series data(时间序列数据)time series data(时间序列数据)time series(时间序列)topic model(主题模型)topic modeling(主题模型)transfer learning 迁移学习triple store 三元组存储uncertainty reasoning 不精确推理undirected graph(无向图)unified modeling language 统一建模语言unsupervisedupper bound(上界)user behavior(用户行为)user generated content(用户生成内容)utility mining(效用挖掘)visual analytics(可视化分析)visual content(视觉内容)visual representation(视觉表征)visualisation(可视化)visualization technique(可视化技术) visualization tool(可视化工具)web 2.0(网络2.0)web forum(web 论坛)web mining(网络挖掘)web of data 数据网web ontology lanuage 网络本体语言web pages(web 页面)web resource 网络资源web science 万维科学web search (网络检索)web usage mining(web 使用挖掘)wireless networks 无线网络world knowledge 世界知识world wide web 万维网world wide web(万维网)xml database 可扩展标志语言数据库附录 2 Data Mining 知识图谱（共包含二级节点15 个，三级节点93 个）间序列分析)监督学习)领域 二级分类 三级分类。
Computational Fluid Dynamics
Computational Fluid Dynamics Computational Fluid Dynamics (CFD) is a branch of fluid mechanics that uses numerical analysis and data structures to solve and analyze problems that involve fluid flows. It has become an essential tool in various industries, including aerospace, automotive, and environmental engineering. CFD allows engineers and scientists to simulate the behavior of fluids in complex systems, such as air flow over an aircraft wing or water flow in a river, without the need for costly and time-consuming physical experiments. One of the key advantages of CFD is itsability to provide detailed insights into fluid flow phenomena that are difficult or impossible to observe experimentally. This is particularly useful in the design and optimization of engineering systems, where understanding the behavior offluids is crucial. For example, CFD can be used to predict the performance of a new aircraft design, optimize the cooling system of a car engine, or analyze the dispersion of pollutants in the atmosphere. By simulating these scenarios, engineers can make informed decisions and improve the efficiency and safety oftheir designs. However, CFD is not without its challenges. One of the main issues is the complexity and computational cost of simulating fluid flows accurately.Fluid dynamics is a highly nonlinear and chaotic phenomenon, and simulating it requires solving complex mathematical equations that describe the behavior of fluids. This often involves dividing the fluid domain into a large number of smaller elements, or "cells," and solving the equations for each cell. As a result, CFD simulations can be computationally intensive and time-consuming, requiringhigh-performance computing resources and specialized software. Another challengeis the accuracy and reliability of CFD simulations. While CFD has made significant advancements in recent years, it is still a numerical approximation of the real physical phenomena. The accuracy of CFD simulations depends on various factors, such as the quality of the mesh (the division of the fluid domain into cells), the choice of numerical methods, and the assumptions and simplifications made in the simulation. Engineers and scientists must carefully validate and verify their CFD simulations against experimental data to ensure their reliability and trustworthiness. Furthermore, CFD requires a deep understanding of fluid mechanics, numerical methods, and computer programming. Engineers and scientistsmust be well-versed in the underlying physics of fluid flows, as well as the mathematical and computational techniques used in CFD. This often requires extensive training and expertise, which can be a barrier for individuals and organizations looking to adopt CFD in their work. Despite these challenges, the potential benefits of CFD make it a valuable tool for engineers and scientists. By providing detailed insights into fluid flow phenomena, CFD enables the design and optimization of engineering systems with improved efficiency and performance. As computing power and simulation techniques continue to advance, CFD is expected to play an increasingly important role in engineering and scientific research, shaping the way we understand and manipulate fluid flows in the world around us.。
Heart Rate Variability：心率变异性
Normal Heart Rate Variability
Beats per minute
time
Plexus
Heart Rate Variability
The Heart Rate cycles in a Wave like pattern over time
A reflection of the behavior of the Cardiovascular System interacting and connected to many other agents
A delayed decrease in the heart rate during the first minute after graded exercise…is a powerful and independent predictor of the risk of death
Cole; NEJM 1999;341:1351-7
– Chaos Theory – Nonlinear Dynamics – Science of Complex Adaptive Systems – Systems Theory
Deals with the behavior and properties of systems
Plexus
System definition
Systems embedded within systems
Plexus
Human Body Interacting with Larger Systems
Nature Ecosystems Solar Cycles Micro-organisms Families, Organizations System embedded within systems
连续和离散动力系统中两类方程的复杂动态
湖南师范大学博士学位论文连续和离散动力系统中两类方程的复杂动态姓名：***申请学位级别：博士专业：基础数学指导教师：***20100501摘要本文应用连续和离散动力系统中的分支理论、二阶平均方法、Ｍｅｌｎｉｋ－ＯＶ方法和混沌理论，首次研究连续和离散动力系统中两类方程当参数变化时不动点的分支、三频率共振解的分支和混沌动态．对于连续动力系统，首先运用Ｍｅｌｎｉｋｏｖ方法和二阶平均方法研究受悬挂轴振动和外力作用的物理单摆在周期扰动下与拟周期扰动下的复杂动态，给出在周期扰动下系统产生混沌运动的准则，在拟周期扰动下，仅能给出当Ｑ＝伽＋Ｅ以ｎ＝１，２，３，４时平均系统存在混沌的条件，而当Ｑ＝ｇｔｏ，；＋ｅ％ｎ＝５—１５时，用平均方法不能给出混沌产生的条件，这里∥和ｕ之比为无理数．同时通过数值模拟，包括二维参数平面和三维参数空间中的分支图，相应的最大Ｌｙａｐｕｎｏｖ指数图，相图以及Ｐｏｉｎｃａｘ色映射，验证了理论结果的正确性，发现了系统的一些复杂动力学行为，其中包括从周期１轨到周期２轨的分支与周期２轨到周期２轨的逆分支；混沌的突然发生：不带周期窗口的全混沌区域，带复杂周期窗口或拟周期窗口的混沌区域；混沌的突然消失，混沌转变成周期１轨；不带周期窗口的全不变环区域或全拟周期轨区域：不变环或拟周期轨突然转变与周期１轨；从一个周期１轨区域到另一个周期１轨区域或从一个拟周期轨区域到另一个拟周期轨区域的突然跳跃；周期１轨的对称断裂：内部危机；发现了许多新颖的混沌吸引子和不变环，等等．数值模拟结果表明：当调整分支参数乜，６，，ｏ与Ｑ的值时，系统动态从全混沌运动或全不变环或全拟周期轨突然转变为周期轨，这有利于控制物理单摆的运动．其次运用二阶平均方法研究受悬挂轴振动和外力作用的物理单摆的三频率共振动解的分支与混沌，运用二阶平均方法研究了当系统的固有频率咖，外力激励频率ｕ与参数频率Ｑ之比：０３０：ｕ：Ｑ≈１：１：佗，１：２：佗，１：３：佗，２：１：仉与３：１：礼时共振解的存在与分支．运用Ｍｅｌｎｉｋｏｖ方法，给出了当ｕｏ：∽：Ｑ≈１：ｍ：佗时共振解存在的条件，并通过数值模拟进行了验证．通过数值模拟，又发现了系统的许多动态，如：不带周期窗口的全不变环行为，不变环区域的串联，不带周期窗口的纯混沌行为，带复杂周期窗口的混沌行为，全周期轨区域；不变环转变为周期轨，周期轨转变为混沌，一种不变环转变为另一种不变环等动态的跳跃行为；内部危机等动态．这些动态与在周期扰动和拟周期扰动下的动态具有很大的差异，特别发现：当初始点由鞍点改变成中心时，有更多的新的不变环吸引子被找到．首次用Ｅｕｌｅｒ方法将细菌培养呼吸过程模型离散化，运用中心流形定理和分支理论，给出映射发生ｆｌｉｐ分支，Ｈｏｐｆ：分支的条件，Ｍａｒｏｔｔｏ意义下的混沌存在的条件，证明映射没有ｆｏｌｄ分支．运用数值模拟方法（包括分支图，相图，最大Ｌｙａｐｕｎｏｖ指数图，分形维数），不仅验证了理论分析结论的正确性，还发现了该映射的许多动态，如：从周期２轨到周期８轨的逆倍周期分支，从周期ｌ轨到周期４轨的逆倍周期分支，带周期窗口的混沌行为，不带周期窗口的全混沌行为，不带周期窗口的全不变环行为，从混沌转变为不变环，从不变环转变为混沌，从混沌转变为周期轨，从周期轨转变为混沌等动态的跳跃，周期轨与混沌的交替行为等．对这两个动力系统的研究，所得到的动态行为将丰富非线性动力系统的内容，对其它学科，例如，化学、物理、生物学的研究有一定的应用价值．全文共分三章．第一章是关于动力系统的分支与混沌的预备知识．简要介绍连续和离散动力系统中的中心流形定理，二阶平均方法、Ｍｅｈａｉｋｏｖ方法以及混沌的定义、特征和通向混沌的道路．第二章，深入分析与研究受悬挂轴振动和外力作用的物理单摆的复杂动态．第二节至第四节，研究在周期扰动下与拟周期扰动下系统的的动态，运用二阶平均方法与Ｍｅｌｎｉｋｏｖ方法，给出系统存在混沌的准则，数值模拟不仅验证了理论分析结果的正确性，发现了系统的一些复杂动力学行为，而且显示当Ｑ＝ｎｏ）＋姒ｎ＝７时系统也存在混沌．本部分的结果发表在ＡｃｔａＭａｔｈｅｍａｔｉｃａＡｐｐｌｉｃａｔａｅＳｉｎａｃａ，ＥｎｇｌｉｓｈＳｅｒｉｅｓ，Ｖ０１．（２６），Ｎｏ．１（２０１０），５５－７８．第五节，研究系统的三频率共振动解的分支与混沌，运用二阶平均方法给出了当系统的固有频率Ｗｏ，外力激励频率ｕ与参数频率Ｑ之比：ｗｏ：ｕ：Ｑ≈１：１：ｎ，１：２：佗，１：３：竹，２：１：ｎ与３：１：ｎ时共振解的存在条件与分支．运用Ｍｅｌｎｉｋｏｖ方法，给出了当Ｗ０：ｕ：Ｑ≈１：仇：ｎ时共振解存在的条件，并通过数值模拟进行了验证．数值模拟又发现了系统的许多动态，显示了与在周期扰动和拟周期扰动下的动态的差异，发现：当初始点由鞍点改变成中心时，有更多的新的不变环吸引子被找到．本部分的结果已被ＡｃｔａＭａｔｈｅｍａｔｉｃａＡｐｐｌｉｃａｔａｅＳｉｎａｃａ，ＥｎｇｌｉｓｈＳｅｒｉｅｓ接收．第三章，研究离散型细菌培养呼吸过程模型．应用欧拉方法将连续型细菌培养呼吸过程模型离散化，运用中心流形定理和分支理论，给出映射发生ｆｌｉｐ分支，Ｈ０ｐ吩支的条件，存在Ｍａｘｏｔｔｏ意义下的混沌的条件，证明系统不存在ｆｏｌｄ分支．运用数值模拟，验证了理论分析结果的正确性，发现了该映射的许多动态．关键词：二阶平均；Ｍｅｌｎｉｋｏｖ方法；分支；混沌；周期扰动；拟周期扰动；三频率共振；Ｍａｘｏｔｔｏ混沌．ＡＢＳＴＲＡＣＴＩｎｔｈｉｓｔｈｅｓｉｓ，ｗｅｉｎｖｅｓｔｉｇａｔｅｓｔｈｅｂｉｆｕｒｃａｔｉｏｎｏｆｆｉｘｅｄｐｏｉｎｔｓａｎｄｒｅｓｏｎａｎｔＳＯ－ｈｉｔｉｏｎｓａｎｄｃｈａｏｓｆｏｒｔｗｏｔｙｐｅｓｏｆｅｑｕａｔｉｏｎｓｉｎｃｏｎｔｉｎｕｏｕｓａｎｄｄｉｓｃｒｅｔｅｄｙｎａｍｉｃａｌｓｙｓｔｅｍｓ，ｗｈｉｃｈａｌｅｎｏｔｃｏｎｓｉｄｅｒｅｄｙｅｔ，ａｓｔｈｅｂｉｆｕｒｃａｔｉｏｎｐａｒａｍｅｔｅｒｓｖａｒｙｂｙａｐ－ｐｌｙｉｎｇｂｉｆｕｒｃａｔｉｏｎｔｈｅｏｒｉｅｓ，ｓｅｃｏｎｄ－ｏｒｄｅｒａｖｅｒａｇｉｎｇｍｅｔｈｏｄ，Ｍｅｌｎｉｋｏｖｍｅｔｈｏｄａｎｄｃｈａｏｓｔｈｅｏｒｙｉｎｃｏｎｔｉｎｕｏｕｓａｎｄｄｉｓｃｒｅｔｅｄｙｎａｍｉｃａｌｓｙｓｔｅｍｓ．Ｆｏｒｔｈｅｃｏｎｔｉｎｕｏｕｓｓｙｓｔｅｍ，ｔｈｅｃｏｍｐｌｅｘｄｙｎａｍｉｃｓｆｏｒｔｈｅｐｈｙｓｉｃａｌｐｅｎｄｕｌｕｍｅｑｕａｔｉｏｎｗｉｔｈｓｕｓｐｅｎｓｉｏｎａｘｉｓｖｉｂｒａｔｉｏｎｓａｒｅｉｎｖｅｓｔｉｇａｔｅｄ．Ｆｉｒｓｔｌｙ＇ｗｅｐｒｏｖｅｔｈｅｃｏｎｄｉｔｉｏｎｓｏｆｅｘｉｓｔｅｎｃｅｏｆｃｈａｏｓｕｎｄｅｒｐｅｒｉｏｄｉｃｐｅｒｔｕｒｂａｔｉｏｎｓｂｙｕｓｉｎｇＭｅｉｎｉｋｏｖ’ｓｍｅｔｈｏｄ．Ｂｙｕｓｉｎｇｓｅｃｏｎｄ－ｏｒｄｅｒａｖｅｒａｇｉｎｇｍｅｔｈｏｄａｎｄＭｅｌｉｎｉｋｏｖ’ｓｍｅｔｈｏｄ．ｗｅｇｉｖｅｔｈｅｃｏｎｄｉｔｉｏｎｓｏｆｅｘｉｓｔｅｎｃｅｏｆｃｈａｏｓｉｎａｖｅｒａｇｅｄｓｙｓｔｅｍｕｎｄｅｒｑｕａｓｉ－ｐｅｒｉｏｄｉｃｐｅｒｔｕｒｂａｔｉｏｎｓｆｏｒＱ＝伽＋ｅ％ｎ＝１—４，ｗｈｅｒｅｌ，ｉｓｎｏｔｒａｔｉｏｎａｌｔｏｏ，ａｎｄｃａｎ’ｔｏｆｃｈａｏｓｆｏｒ佗＝５—１５．ａｎｄｃａｌｌｓｈｏｗｔｈｅｃｈａｏｔｉｃｐｒｏｖｅｔｈｅｃｏｎｄｉｔｉｏｎｏｆｅｘｉｓｔｅｎｃｅｂｅｈａｖｉｏｒｓｆｏｒｎ＝５ｂｙｎｕｍｅｒｉｃａｌｓｉｍｕｌａｔｉｏｎｓ．Ｂｙｎｕｍｅｒｉｃａｌｓｉｍｕｌａｔｉｏｎｓｉｎｃｌｕｄｉｎｇｂｉｆｕｒｃａｔｉｏｎｄｉａｇｒａｍｓ，ｐｈａｓｅｐｏｒｔｒａｉｔｓ，ｃｏｍｐｕｔａｔｉｏｎｏｆｍａｘｉｍｕｍＬｙａｐｕｎｏｖｅｘｐｏ－ｎｅｎｔｓａｎｄＰｏｉｎｃａｌｇｍａｐ，ｗｅｃｈｅｃｋｕｐｔｈｅｅｆｆｅｃｔｏｆｔｈｅｏｒｅｔｉｃａｌａｎａｌｙｓｉｓａｎｄｅｘｐｏｓｅｔｈｅｃｏｍｐｌｅｘｄｙｎａｍｉｃａｌｂｅｈａｖｉｏｒｓ，ｉｎｃｌｕｄｉｎｇｔｈｅｂｉｆｕｒｃａｔｉｏｎａｎｄｒｅｖｅｒｓｅｂｉｆｕｒｃａ－ｔｉｏｎｆｒｏｍｐｅｒｉｏｄ－ｏｎｅｔｏｐｅｒｉｏｄ—ｔｗｏｏｒｂｉｔｓ；ａｎｄｔｈｅｏｎｓｅｔｏｆｃｈａｏｓ，ａｎｄｔｈｅｅｎｔｉｒｅｃｈａｏｔｉｃｒｅｇｉｏｎｗｉｔｈｏｕｔｐｅｒｉｏｄｉｃｗｉｎｄｏｗｓ，ｃｈａｏｔｉｃｒｅｇｉｏｎｓｗｉｔｈｃｏｍｐｌｅｘｐｅｒｉｏｄｉｃｗｉｎｄｏｗｓｏｒｗｉｔｈｃｏｍｐｌｅｘｑｕａｓｉ—ｐｅｒｉｏｄｉｃｗｉｎｄｏｗｓ；ｃｈａｏｔｉｃｂｅｈａｖｉｏｒｓｓｕｄｄｅｎｌｙｄｉｓ－ａｐｐｅａｒｉｎｇ，ｏｒｃｏｎｖｅｒｔｉｎｇｔｏｐｅｒｉｏｄ－ｏｎｅｏｒｂｉｔｗｈｉｃｈｍｅａｎｓｔｈａｔｔｈｅｓｙｓｔｅｍｃａｎｂｅｓｔａｂｉｌｉｚｅｄｔｏｐｅｒｉｏｄｉｃｍｏｔｉｏｎｂｙａｄｊｕｓｔｉｎｇｂｉｆｕｒｃａｔｉｏｎｐａｒａｍｅｔｅｒｓ口，最ｆ０ａｎｄｆｌ；ａｎｄｔｈｅｏｎｓｅｔｏｆｉｎｖａｒｉａｎｔｔｏｍｓｏｒｑｕａｓｉ－ｐｅｒｉｏｄｉｃｂｅｈａｖｉｏｒｓ，ｔｈｅｅｎｔｉｒｅｉｎｖａｒｉ－ａｎｔｔｏｍｓｒｅｇｉｏｎｏｒｑｕａｓｉ－ｐｅｒｉｏｄｉｃｒｅｇｉｏｎｗｉｔｈｏｕｔｐｅｒｉｏｄｉｃｗｉｎｄｏｗ，ｑｕａｓｉ－ｐｅｒｉｏｄｉｃｂｅｈａｖｉｏｒｓｏｒｉｎｖａｒｉａｎｔｔｏｒｕｓｂｅｈａｖｉｏｒｓｍ：ｔｄｄｅｎｌｙｄｉｓａｐｐｅａｒｉｎｇｏｒｃｏｎｖｅｒｔｉｎｇｔｏｐｅ－ｒｉｏｄｉｃｏｒｂｉｔ；ａｎｄｔｈｅｊｕｍｐｉｎｇｂｅｈａｖｉｏｒｓｗｈｉｃｈｉｎｃｌｕｄｉｎｇｆｒｏｍｐｅｒｉｏｄ—ｏｎｅｏｒｂｉｔｔｏａｎｔｈｅｒｐｅｒｉｏｄ－ｏｎｅｏｒｂｉｔ，ｆｒｏｍｑｕａｓｉ—ｐｅｒｉｏｄｉｃｓｅｔｔｏａｎｏｔｈｅｒｑｕａｓｉ－ｐｅｒｉｏｄｉｃｓｅｔ；ａｎｄｔｈｅｉｎｔｅｒｌｅａｖｉｎｇｏｃｃｕｒｒｅｎｃｅｏｆｃｈａｏｔｉｃｂｅｈａｖｉｏｒｓａｎｄｉｎｖａｌｉａｎｔｔｏｒｕｓｂｅｈａｖｉｏｒｓｏｒｑｕａｓｉ—ｐｅｒｉｏｄｉｃｂｅｈａｖｉｏｒｓ；ａｎｄｔｈｅｉｎｔｅｒｉｏｒｃｒｉｓｉｓ；ａｎｄｔｈｅｓｙｍｍｅｔｒｙｂｒｅａｋｉｎｇｏｆＩＶａｎｄｉｎｖａｒｉａｎｔｔｏｍｓ．Ｉｎｐｅｒｉｏｄ－ｏｎｅｏｒｂｉｔ；ａｎｄｔｈｅｄｉｆｆｅｒｅｎｔｎｉｃｅｃｈａｏｔｉｃａｔｔｒａｃｔｏｒｓｐａｒｔｉｃｕｌａｒ，ｔｈｅｓｙｓｔｅｍｓｈｏｗｎｔｈｅｅｎｔｉｒｅｃｈａｏｔｉｃｒｅｇｉｏｎｏｒｉｎｖａｒｉａｎｔｔｏｍｓｒｅｇｉｏｎｏｒｅｎｔｉｒｅｑｕａｓｉ－ｐｅｒｉｏｄｉｃｒｅｇｉｏｎｓｕｄｄｅｎｌｙｃｏｎｖｅｒｔｉｎｇｔｏｐｅｒｉｏｄｉｃｏｒｂｉｔｂｙａｄｊｕｓｔｉｎｇｔｈｅｂｉｆｕｒｃａｔｉｏｎｐａｒａｍｅｔｅｒｓＱ，正／０ａｎｄＱ，ｗｈｉｃｈｉｓｂｅｎｅｆｉｃｉａｌｔｏｔｈｅｃｏｎｔｒｏｌｏｆｍｏｔｉｏｎｓｏｆｔｈｅｐｅｎｄｕｌｕｍ．ｂｉｆｕｒｃａｔｉｏｎｓｏｆｒｅｓｏｎａｎｔｓｏｌｕ—Ｓｅｃｏｎｄｌｙ，ｗｅｉｎｖｅｓｔｉｇａｔｅｔｈｅｅｘｉｓｔｅｎｃｅａｎｄｔｈｅｔｉｏｎｆｏｒｗ０：ｕ：Ｑ≈１：１：佗，１：２：佗，１：３：ｎ，２：１：ｔｌａｎｄ３：１：扎ｂｙｕｓｉｎｇｓｅｃｏｎｄ－ｏｒｄｅｒａｖｅｒａｇｉｎｇｍｅｔｈｏｄａｎｄｇｉｖｅａｃｒｉｔｅｒｉｏｎｆｏｒｔｈｅｅｘｉｓｔｅｎｃｅｏｆｒｅｓｏｎａｎｔｓｏｌｕｔｉｏｎｆｏｒｗ０：ｕ：Ｑ≈１：仇：ｆｌｉｓｇｉｖｅｎｂｙｕｓｉｎｇＭｅｌｎｉｋｏｖ’Ｓｍｅｔｈｏｄａｎｄｖｅｒｉｆｙｔｈｅｔｈｅｏｒｅｔｉｃａｌａｎａｌｙｓｉｓｂｙｎｕｍｅｒｉｃａｌｓｉｍｕｌａｔｉｏｎｓ．Ｂｙｎｕｍｅｒｉｃａｌｓｉｍｕｌａｔｉｏｎ，ｗｅｓｏｍｅｏｔｈｅｒｉｎｔｅｒｅｓｔｉｎｇｄｙｎａｍｉｃａｌｂｅｈａｖｉｏｒｓ，ｉｎｃｌｕｄｉｎｇｔｈｅｅｎｔｉｒｅｉｎｖａｒｉａｎｔｅｘｐｏｓｅｔｏｍｓｒｅｇｉｏｎ，ｔｈｅｃａｓｃａｄｅｏｆｉｎｖａｒｉａｎｔｔｏｒｕｓｂｅｈａｖｉｏｒｓ，ｔｈｅｅｎｔｉｒｅｃｈａｏｓｒｅｇｉｏｎｗｉｔｈ—ｏｕｔｐｅｒｉｏｄｉｃｗｉｎｄｏｗｓ，ｃｈａｏｔｉｃｒｅｇｉｏｎｗｉｔｈｃｏｍｐｌｅｘｐｅｒｉｏｄｉｃｗｉｎｄｏｗｓ，ｔｈｅｅｎｔｉｒｅｗｈｉｃｈｉｎｃｌｕｄｉｎｇｉｎｖａｒｉａｎｔｔｏｒｕｓｐｅｒｉｏｄ－ｏｎｅｏｒｂｉｔｓｒｅｇｉｏｎ；ｔｈｅｊｕｍｐｉｎｇｂｅｈａｖｉｏｒｓｂｅｈａｖｉｏｒｓｃｏｎｖｅｒｔｉｎｇｔｏｐｅｒｉｏｄ－ｏｎｅｏｒｂｉｔｓ，ｆｒｏｍｃｈａｏｓｔｏｉｎｖａｒｉａｎｔｔｏｒｕｓｂｅｈａｖｉｏｒｓｏｒｆｒｏｍｉｎｖａｒｉａｎｔｔｏｍｓｂｅｈａｖｉｏｒｓｔｏｃｈａｏｓ，ｆｒｏｍｐｅｒｉｏｄ－ｏｎｅｔｏｃｈａｏｓ，ｆｒｏｍｉｎｖａｒｉａｎｔｔｏｍｓｂｅｈａｖｉｏｒｓｔｏａｎｏｔｈｅｒｉｎｖａｒｉａｎｔｔｏｍｓｂｅｈａｖｉｏｒｓ；ａｎｄｔｈｅｉｎｔｅｒｉｏｒｃｒｉｓｉｓ；ａｎｄｔｈｅｄｉｆｆｅｒｅｎｔｎｉｃｅｉｎｖａｒｉａｎｔｔｏｒｕｓａｔｔｒａｃｔｏｒｓａｎｄｃｈａｏｔｉｃａｔｔｒａｃｔｏｒｓ．Ｔｈｅｎｕｍｅｒｉｃａｌｒｅｓｕｌｔｓｓｌｉｏｗｔｈｅｄｉｆｆｅｒｅｎｃｅｏｆｄｙｎａｍｉｃａｌｂｅｈａｖｉｏｒｓｉｎｔｈｅｐｈｙｓｉｃａｌｐｅｎｄｕｌｕｍｅｑｕａ－ｔｉｏｎｗｉｔｈｓｕｓｐｅｎｓｉｏｎａｘｉｓｖｉｂｒａｔｉｏｎｓｂｅｔｗｅｅｎｕｎｄｅｒｔｈｅｔｈｒｅｅｆｒｅｑｕｅｎｃｉｅｓｒｅｓｏｎａｎｔａｎｄｕｎｄｅｒｔｈｅｐｅｒｉｏｄｉｃ／ｑｕａｓｉ—ｐｅｒｉｏｄｉｃｐｅｒｔｕｒｂａｔｉｏｎｓ．Ｉｔｅｘｈｉｂｉｔｓｍａｎｙｃｏｎｄｉｔｉｏｎｎｉｃｅｉｎｖａｒｉａｎｔｔｏｒｕｓｂｅｈａｖｉｏｒｓｕｎｄｅｒｔｈｅｒｅｓｏｎａｎｔｃｏｎｄｉｔｉｏｎｓａｎｄｗｅｆｉｎｄａｌｏｔｏｆｃｈａｏｔｉｃｂｅｈａｖｉｏｒｓｗｈｉｃｈａｒｅｄｉｆｆｅｒｅｎｔｔｏｔｈｏｓｅｕｎｄｅｒｔｈｅｐｅｒｉｏｄｉｃ／ｑｕａｓｉ—ｐｅｒｉｏｄｉｃｐｅｒｔｕｒｂａｔｉｏｎｓ．Ｆｏｒｔｈｅｄｉｓｃｒｅｔｅｓｙｓｔｅｍ，ｔｈｅｄｙｎａｍｉｃａｌｂｅｈａｖｉｏｒｓｏｆａｄｉｓｃｒｅｅｔｍａｔｈｅｍａｔｉｃａｌｍｏｄｅｌｆｏｒｒｅｓｐｉｒａｔｏｒｙｐｒｏｃｅｓｓｉｎｂａｃｔｅｒｉａｌｃｕｌｔｕｒｅａｒｅｉｎｖｅｓｔｉｇａｔｅｄ．ＴｈｅｃｏｎｄｉｔｉｏｎｓｏｆｅｘｉｓｔｅｎｃｅｆｏｒｆｌｉｐｂｉｆｕｒｃａｔｉｏｎａｎｄＨｏｐｆｂｉｆｕｒｃａｔｉｏｎａｒｅｄｅｒｉｖｅｄｂｙｕｓｉｎｇｃｅｎ－ｔｅｒｍａｎｉｆｏｌｄｔｈｅｏｒｅｍａｎｄｂｉｆｕｒｃａｔｉｏｎｔｈｅｏｒｙ，ｃｏｎｄｉｔｉｏｎｏｆｅｘｉｓｔｅｎｃｅｏｆｃｈａｏｓｉｎｔｈｅＳｅｌｚ．ｑｅｏｆＭａｒｏｔｔｏ’８ｄｅｆｉｎｉｔｉｏｎｏｆｃｈａｏｓｉｓｐｒｏｖｅｄ．Ｔｈｅｂｉｆｕｒｃａｔｉｏｎｄｉａｇｒａｍｓ，ＶＬｙａｐｕｎｏｖｅｘｐｏｎｅｎｔｓａｎｄｐｈａｓｅｐｏｒｔｒａｉｔｓａｒｅｇｉｖｅｎｆｏｒｄｉｆｆｅｒｅｎｔｐａｒａｍｅｔｅｒｓｏｆｔｈｅｍｏｄｅｌ，ａｎｄｔｈｅｆｒａｃｔａｌｄｉｍｅｎｓｉｏｎｏｆｃｈａｏｔｉｃａｔｔｒａｃｔｏｒｏｆｔｈｅｍｏｄｅｌｉｓａｌｓｏｃａｌｃｕ－ｉａｔｅｄ．Ｔｈｅｎｕｍｅｒｉｃａｌｓｉｍｕｌａｔｉｏｎｒｅｓｕｌｔｓｎｏｔｏｎｌｙｓｈｏｗｔｈｅｃｏｎｓｉｓｔｅｎｃｅｗｉｔｈｔｈｅｔｈｅｏｒｅｔｉｃａｌａｎａｌｙｓｉｓｂｕｔａｌｓｏｄｉｓｐｌａｙｔｈｅｎｅｗａｎｄｉｎｔｅｒｅｓｔｉｎｇｃｏｍｐｌｅｘｄｙｎａｍｉｃａｌｂｅｈａｖｉｏｒｓｃｏｍｐａｒｅｄｗｉｔｈｔｈｅｃｏｎｔｉｍｌｏｕｓｍｏｄｅｌ，ｉｎｃｌｕｄｉｎｇｒｅｖｅｒｓｅｂｉｆｉｌｒｃａｔｉｏｎｆｒｏｍｐｅｒｉｏｄ—ｔｗｏｔｏｐｅｒｉｏｄ－ｅｉｇｈｔｏｒｂｉｔｓａｎｄｆｒｏｍｐｅｒｉｏｄ－ｏｎｅｏｒｂｉｔｓｔｏｐｅｒｉｏｄ－ｆｏｕｒｏｒｂｉｔｓ，ｔｈｅｃａｓｃａｄｅｓｏｆｐｅｒｉｏｄ—ｄｏｕｂｌｉｎｇｂｉｆｕｒｃａｔｉｏｎｓｆｒｏｍｐｅｒｉｏｄ－ｏｎｅｏｒｂｉｔｓｔｏｐｅｒｉｏｄ—ｅｉｇｈｔｏｒｂｉｔｓａｎｄｆｒｏｍｐｅｒｉｏｄ－ｔｈｒｅｅｏｒｂｉｔｓｔｏｐｅｒｉｏｄ—ｔｗｅｌｖｅｏｒｂｉｔｓ；ａｎｄｔｈｅｏｎｓｅｔｏｆｃｈａｏｓ，ａｎｄｔｈｅｅｎｔｉｒｅｃｈａｏｔｉｃｒｅｇｉｏｎｗｉｔｈｏｕｔｐｅｒｉｏｄｉｃｗｉｎｄｏｗｓ，ｃｈａｏｔｉｃｒｅｇｉｏｎｓｗｉｔｈｃｏｉｎ－ｐｌｅｘｐｅｒｉｏｄｉｃｗｉｎｄｏｗｓ，ｔｈｅｅｎｔｉｒｅｉｎｖａｒｉａｎｔｔｏｒｍｓｗｉｔｈｏｕｔｐｅｒｉｏｄｉｃｗｉｎｄｏｗｓ；ｃｈａｏｔｉｃｂｅｈａｖｉｏｒｓｃｏｎｖｅｒｔｉｎｇｔｏｐｅｒｉｏｄｉｃｏｒｂｉｔｓ；ａｎｄｔｈｅｊｕｍｐｉｎｇｂｅｈａｖｉｏｒｓｉｎｃｌｕｄｉｎｇｆｒｏｍｃｈａｏｓｔｏｉｎｖａｒｉａｎｔｔｏｍｓ，ｆｒｏｍｉｎｖａｒｉａｎｔｔｏｍｓｔｏｃｈａｏｓａｎｄｆｒｏｍｐｅｒｉｏｄｉｃｏｒｂｉｔｓｔｏｃｈａｏｓ；ａｎｄｔｈｅｉｎｔｅｒｌｅａｖｉｎｇｏｃｃｕｒｒｅｎｃｅｏｆｐｅｒｉｏｄｉｃｏｒｂｉｔｓａｎｄｉｎｖａｒｉａｎｔｔｏｍｓｂｅｈａｖｉｏｒｓ；ａｎｄｔｈｅｄｉｆｆｅｒｅｎｔｎｉｃｅｃｈａｏｔｉｃａｔｔｒａｃｔｏｒｓａｎｄｉｎｖａｒｉａｎｔｔｏｒｕｓ．Ｔｈｅｓｔｕｄｙｆｏｒｔｈｅｍｉｓｏｆｆｕｎｄａｍｅｎｔａｌａｎｄｅｖｅｎｐｒａｃｔｉｃａｌｉｎｔｅｒｅｓｔ．ＴｈｅｄｙｎａｍｉｃａｌｂｅｈａｖｉｏｒｓｏｆｔｈｅｓｅＳｙｓｔｅｍ８ｗｉｌｌｅｎｒｉｃｈｔｈｅｃｏｎｔｅｎｔｏｆｎｏｎｌｉｎｅａｒｄｙｎａｍｉｃａｌｓｙｓｔｅｍｓａｎｄｗｉｌｌｂｅｕｓｅｆｕｌｉｎｏｔｈｅｒｓｕｂｊｅｃｔｓｓｕｃｈａｓｃｈｅｍｉｓｔｒｙ，ｐｈｙｓｉｃｓａｎｄｂｉｏｌｏｇｙ．Ｔｈｉｓｔｈｅｓｉｓｃｏｎｓｉｓｔｓｏｆｔｈｒｅｅｃｈａｐｔｅｒｓａｓｔｈｅｆｏｌｌｏｗｉｎｇ．Ｃｈａｐｔｅｒ１ｉｓａｂｏｕｔｐｒｅｐａｒａｔｉｏｎｋｎｏｗｌｅｄｇｅ．Ａｂｒｉｅｆｒｅｖｉｅｗｏｆｃｅｎｔｅｒｍａｎｉｆｏｌｄｔｈｅｏｒｅｍｓｆｏｒｃｏｎｔｉｎｕｍｍａｎｄｄｉｓｃｒｅｔｅｄｙｎａｍｉｃａｌｓｙｓｔｅｍｉｓｐｒｅｓｅｎｔｅｄ．Ａｔｔｈｅ８ａ工ｎｅｔｉｍｅ，ｓｏｍｅｄｅｆｉｎｉｔｉｏｎｓａｎｄｃｈａｒａｃｔｅｒｉｓｔｉｃｓｏｆｃｈａｏｓａｓｗｅｌｌ晒ｓｏｍｅｒｏｕｔｅｓｔｏｃｈａｏｓａｒｅｍｅｎｔｉｏｎｅｄ．Ｉｎｃｈａｐｔｅｒ２，ｔｈｅｐｈｙｓｉｃａｌｐｅｎｄｕｌｕｍｅｑｕａｔｉｏｎｗｉｔｈｓｕｓｐｅｎｓｉｏｎａｘｉｓｖｉｂ胁ｔｉｏｎｓｉｓｉｎｖｅｓｔｉｇａｔｅｄ．Ｉｎｓｅｃｔｉｏｎ２．２，２．３ａｎｄ２．４，ｔｈｅｃｏｎｄｉｔｉｏｎｓｏｆｅｘｉｓｔｅｎｃｅｏｆｃｈａｏｓｕｎｄｅｒｐｅｒｉｏｄｉｃｐｅｒｔｕｒｂａｔｉｏｎｓａｎｄｕｎｄｅｒｑｕａｓｉ—ｐｅｒｉｏｄｉｃｐｅｒｔｕｒｂａｔｉｏｎｓａｒｅｇｉｖｅｎｂｙｕｓｉｎｇＭｅｌｎｉｋｏｖ’Ｓｍｅｔｈｏｄａｎｄｓｅｃｏｎｄ—ｏｒｄｅｒａｖｅｒａｇｉｎｇｍｅｔｈｏｄ．Ｂｙｎｕ－ｍｅｒｉｃａｌｓｉｍｕｌａｔｉｏｎｓｗｅｎｏｔｏｎｌｙｃｈｅｃｋｕｐｔｈｅｅｆｆｅｃｔｏｆｔｈｅｏｒｅｔｉｃａｌａｎａｌｙｓｉｓａｎｄｅｘｐｏｓｅｔｈｅｃｏｍｐｌｅｘｄｙｎａｍｉｃａｌｂｅｈａｖｉｏｒｓ，ｂｕｔａｌｓｏｓｈｏｗｔｈｅｃｈａｏｔｉｃｂｅｈａｖｉｏｒｓａ８ＶＩＱ＝删＋ｆ％ｎ＝７．Ｉｎｓｅｃｔｉｏｎ２．５，ｗｅｉｎｖｅｓｔｉｇａｔｅｔｈｅｅｘｉｓｔｅｎｃｅａｎｄｔｈｅｂｉｆｕｒｃａ－ｔｉｏｎｓｏｆｒｅｓｏｎａｎｔｓｏｌｕｔｉｏｎｆｏｒ峋：ｕ：Ｑ≈１：１：佗，１：２：佗，１：３：佗，２：１：ｎａｎｄ３：１：，ｌｂｙｕｓｉｎｇｓｅｃｏｎｄ－ｏｒｄｅｒａｖｅｒａｇｉｎｇｍｅｔｈｏｄａｎｄｇｉｖｅａｃｒｉｔｅｒｉｏｎｆｏｒｔｈｅｅｘｉｓ－ｔｅｎｃｅｏｆｒｅｓｏｎａｎｔｓｏｌｕｔｉｏｎｆｏｒ岫：ｕ：Ｑ≈１：仇：礼ｉｓｇｉｖｅｎｂｙｕｓｉｎｇＭｅｉｎｉｋ＿ｏｖ’ｓｍｅｔｈｏｄａｎｄｖｅｒｉｆｙｔｈｅｔｈｅｏｒｅｔｉｃａｌａｎａｌｙｓｉｓｂｙｎｕｍｅｒｉｃａｌｓｉｍｕｌａｔｉｏｎｓ．Ｂｙｍｌｍｅｒｉｃａｌｓｉｍｕｌａｔｉｏｎ，ｗｅｅｘｐｏｓｅｓｏｍｅｏｔｈｅｒｉｎｔｅｒｅｓｔｉｎｇｄｙｎａｍｉｃａｌｂｅｈａｖｉｏｒｓ．Ｔｈｅｍｌｍｅｒｉｃａｌｒｅｓｕｌｔｓｓｈｏｗｔｈｅｄｉｆｆｅｒｅｎｃｅｏｆｄｙｎａｍｉｃａｌｂｅｈａｖｉｏｒｓｉｎｔｈｅｐｈｙｓｉｃａｌｐｅｎｄｕｌｕｍｅｑｕａ－ｔｉｏｎｗｉｔｈｓｕｓｐｅｎｓｉｏｎａｘｉｓｖｉｂｒａｔｉｏｎｓｂｅｔｗｅｅｎｕｎｄｅｒｔｈｅｔｈｒｅｅｆｒｅｑｕｅｎｃｉｅｓｒｅｓｏｎａｎｔｃｏｎｄｉｔｉｏｎａｎｄｕｎｄｅｒｔｈｅｐｅｒｉｏｄｉｃ／ｑｕａｓｉ—ｐｅｒｉｏｄｉｃｐｅｒｔｕｒｂａｔｉｏｎｓ．Ｉｔｅｘｈｉｂｉｔｓｍａｎｙｎｉｃｅｉｎｖａｒｉａｎｔｔｏｒｕｓｂｅｈａｖｉｏｒｓｕｎｄｅｒｔｈｅｒｅｓｏｎａｎｔｃｏｎｄｉｔｉｏｎｓａｎｄｗｅｆｉｎｄａｌｏｔｏｆｃｈａｏｔｉｃｂｅｈａｖｉｏｒｓｗｈｉｃｈａｒｅｄｉｆｆｅｒｅｎｔｔｏｔｈｏｓｅｕｎｄｅｒｔｈｅｐｅｒｉｏｄｉｃ／ｑｕａｓｉ·ｐｅｒｉｏｄｉｃｐｅｒｔｕｒｂａｔｉｏｎｓ．Ｉｎｃｈａｐｔｅｒ３，ｔｈｅｄｙｎａｍｉｃａｌｂｅｈａｖｉｏｒｓｏｆａｄｉｓｃｒｅｅｔｍａｔｈｅｍａｔｉｃａｌｍｏｄｅｌｆｏｒｔｈｅｒｅｓｐｉｒａｔｏｒｙｐｒｏｃｅｓｓｉｎｂａｃｔｅｒｉａｌｃｕｌｔｕｒｅａｒｅｉｎｖｅｓｔｉｇａｔｅｄ．ＴｈｅｃｏｎｄｉｔｉｏｎｓｏｆｅｘｏｉｓｔｅｎｃｅｆｏｒｆｌｉｐｂｉｆｕｒｃａｔｉｏｎａｎｄＨｏｐｆｂｉｆｕｒｃａｔｉｏｎａｒｅｄｅｒｉｖｅｄｂｙｕｓｉｎｇｃｅｎｔｅｒｍａｕｌ－ｆｏｌｄｔｈｅｏｒｅｍａｎｄｂｉｆｕｒｃａｔｉｏｎｔｈｅｏｒｙ，ａｎｄｗｅｐｒｏｖｅｔｈａｔｔｈｅｒｅｉｓｎｏｆｏｌｄｂｉｆｕｒｃａｔｉｏｎ．ＴｈｅｃｈａｏｔｉｃｅｘｉｓｔｅｎｃｅｉｎｔｈｅｓｅｎｓｅｏｆＭａｒｏｔｔｏ’Ｓｄｅｆｉｎｉｔｉｏｎｏｆｃｈａｏｓｉｓｐｒｏｖｅｄ．Ｔｈｅｎｕｍｅｒｉｃａｌｓｉｍｕｌａｔｉｏｎｒｅｓｕｌｔｓｄｉｓｐｌａｙｓｏｍｅｎｅｗａｎｄｃｏｍｐｌｅｘｄｙｎａｍｉｃａｌｂｅｈａｖｉｏｒｓ．Ｋｅｙｗｏｒｄｓ：ｓｅｃｏｎｄ－ｏｒｄｅｒａｖｅｒａｇｉｎｇｍｅｔｈｏｄ，Ｍｅｌｎｉｋｏｖ’８ｍｅｔｈｏｄ，ｂｉｆｕｒ－ｃａｔｉｏｎ，ｃｈａｏｓ，ｐｅｒｉｏｄｉｃｐｅｒｔｕｒｂａｔｉｏｎｓ，ｑｕａｓｉ－ｐｅｒｉｏｄｉｃｐｅｒｔｕｒｂａｔｉｏｎｓ，Ｍａｒｏｔｔｏ’Ｓｃｈａｏｓ．ＶＩＩ湖南师范大学学位论文原创性声明本人郑重声明：所呈交的学位论文，是本人在导师的指导下，独立进行研究工作所取得的成果．除文中已经注明引用的内容外，本论文不含任何其他个人或集体已经发表或撰写过的作品成果．对本文的研究做出重要贡献的个人和集体，均已在文中以明确方式标明．本人完全意识到本声明的法律结果由本人承担．靴论文作者躲槲＂年‘且ｙ日湖南师范大学学位论文版权使用授权书本学位论文作者完全了解学校有关保留、使用学位论文的规定，研究生在校攻读学位期间论文工作的知识产权单位属湖南师范大学．同意学校保留并向国家有关部门或机构送交论文的复印件和电子版，允许论文被查阅和借阅．本人授权湖南师范大学可以将学位论文的全部或部分内容编入有关数据库进行检索，可以采用影印、缩印或扫描等复制手段保存和汇编本学位论文．本学位论文属于·１、保密口，在——年解密后适用本授权书．２、不保密ｄ（请在以上相应方框内打“￣／＂）作者签名：导师签名：１４７日瓣纱秘片咱日勘沙年６月∥汨连续和离散动力系统中两类方程的复杂动态１．预备知识１．１动力系统概述及其定义动力系统的研究来源于常微分方程定性理论．考虑舻中的常微分方程（组）圣＝，（卫），（１．１．１）其中，ｚ＝（ｚ。
非线性领域著名的期刊
非线性领域著名的期刊
1 Complexity 3.514
2 PLoS one 3.057
3 Nonlinear Dynamics 3.0
4 Communications in Nonlinear Science and Numerical Simulation 2.834
26 Journal of Nonlinear Sciences and Applications 1.176
27 Nonlinear Analysis- Theory Methods and Applications 1.125
28 Nonlinear Analysis-Modelling and Contr 2.392
6 Physical Review E 2.252
7 Chaos 2.049
8 EPL 1.963
9 Physica a-Statistical Mechanics and Its Applications 1.785
10 Chaos Solitons & Fractals 1.611
29 Journal of Nonlinear Mathematical Physics 0.580
30 Journal of Biological Dynamics 1.147
31
Applied Mathematics and Computing 1.345
32 Applied Mathematical Modelling 2.291
33 Mathematical Modelling and Analysis 0.468
34 Journal of Vibration and Control 1.643
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• Local randomness vs. global stability • Deterministic – not total disorder
Chaos (cont.)
• Consider a non-linear converge, enter into periodic motion, or enter into chaotic motion
– Nonlinear – Unsmooth – Random
Chaos
• Random results from simple equations OR • Finding order in random results
• Sensitivity to initial conditions
– Butterfly effect – Measurement issues (parameter uncertainty)
• Kepler (1571-1630 AD)
– Originally tried to place planetary orbits within a framework of “nested solids” – Ultimately, determined that planets orbit according to ellipses
Agenda
• • • • • • • Purpose and framework Historical background Chaos and complexity Nonlinear modeling techniques Sample references Contact information Questions / ideas / suggestions
– Entropy = disorder
– Second law of thermodynamics
Quotation
Nonlinear Dynamics and Chaos: Where do we go from here? (Preface) “This book was born out of the lingering suspicion that the theory and practice of dynamical systems had reached a plateau of development…. The over-riding message is clear: if dynamical systems theory is to make a significant long-term impact, it needs to get smart, because most systems are ill-defined….”
Purpose and Framework
• What this presentation is
– Description of historical evolution – An overview of concepts – Hopefully, inspirational
• What this presentation is not
So….
• We naturally (and/or have been conditioned to) love and accept
– Linearity – Smoothness – Stability
• This, in the face of a world that is largely
• One particular (very good) student asked recently
– “How do I know I won’t get bored with being an actuary,” which morphed into – “Where is the beauty in actuarial science?”
– – – – – – Cognitive neuroscience Computation in physical and biological systems Economic and social interactions Evolutionary dynamics Network dynamics Robustness
Historical Background (cont.)
• Copernicus (1473-1543 AD)
– Heliocentric universe – Planetary movements still circular – Complicated: 48 cycles and epicycles
• In a fast-changing, dynamic world, the profession must also evolve and adapt to the underlying factors
Historical Background
• Plato (427-347 BC)
– Forms, Ideas, Ideals – Eternal, absolute, unchanging – Outside the sense-world
Complexity
• A commonly heard definition: “the edge of chaos”
– Between order and randomness
• Simple rules can lead to complex systems
• Related to “entropy”
Historical Background (cont.)
• Euclid (c. 300 BC)
– Compiled mathematical thought into his Elements – Systematized theorem and methodology of proof, as well as geometric reasoning (which held primacy until quite recently)
Purpose and Framework (cont.)
A Personal Anecdote
• Some common student questions
– – – – “Will this be on the exam?” “Is the final cumulative?” “What do I say at an interview?” “How do I decide between casualty and life?”
Sante Fe Institute
• • • • • Founded in 1984 Private, non-profit Multidisciplinary research and education Primarily a “visiting” institution Current research focus areas
Nonlinear Dynamics and Complex Systems
Rick Gorvett, FCAS, MAAA, ARM, FRM, Ph.D. Actuarial Science Professor University of Illinois at Urbana-Champaign ERM Symposium Chicago, IL April 2004
Historical Background (cont.)
• Nineteenth-century
– Non-Euclidean geometry: space need not be “flat”
• Twentieth-century
– Relativity: space-time is warped by matter and energy – Quantum mechanics: probabilistic; breakdown of causality principle
• Pythagoras (570-490 BC)
– Leader of a religious sect – Numbers are primary – Relationship between plucked string length and the resulting musical note – Pythagorean theorem, etc.
– A cookbook of tried-and-true formulas – An encyclopedia of applications
• This material is much more a way of thinking than rote application of equations and techniques
Quotation
War and Peace, by Leo Tolstoy
Book Eleven, Chapter 1
“Only by taking infinitesimally small units for observation (the differential of history, that is, the individual tendencies of men) and attaining to the art of integrating them (that is, finding the sum of these infinitesimals) can we hope to arrive at the laws of history.”
• Example: the logistic function