复杂网络中的同步

Collective synchronization was first studied mathematically by Wiener, who recognized its ubiquity in the natural world, and who speculated that it was involved in the generation of alpha rhythms in the brain. Unfortunately, Wiener’s mathematical approach based on Fourier integrals has turned out to be a dead end.
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2. Exploring the Onset of Synchronization

An ongoing tale full of twists and turns. Earlier works raised more questions than they answered.

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Norbert Wiener
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Harmful Synchronization in Internet
TCP window increase/decrease cycles Synchronization occurs when separate TCP connections share a common bottleneck router Synchronization to an external clock Two processes can become synchronized simply if they are both synchronized to the same external clock Client-server models Multiple clients can become synchronized as they wait for services from a busy (or recovering) server Periodic routing messages Periodic routing messages from different routers can become synchronized
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Synchronization may be harmful……
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Pedestrians make London’s Millennium Bridge wobble
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Tacoma Narrows Bridge Disaster

On November 7, 1940, at approximately 11:00 AM, the first Tacoma Narrows suspension bridge collapsed due to wind-induced vibrations. Situated on the Tacoma Narrows in Puget Sound, near the city of Tacoma, Washington, the bridge had only been open for traffic a few months.
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Synchronization of Periodic Routing Messages
Routers
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Hosts
What’s the connection of all these synchronization phenomena?




On the surface, they might seem unrelated. After all, the forces that synchronize fireflies have nothing to do with those in a laser. But at a deeper level, there is a connection, one that transcends the details of any particular mechanism. That connection is mathematics. All the examples are variations on the same mathematical theme: self-organization, the spontaneous emergence of order out of chaos. Scientists are beginning to unlock the secrets of this dazzling kind of order in the universe.

汪小帆教授，李翔博士 博士后1名 博பைடு நூலகம்生8名 硕士生10名
研究课题： 混沌控制、同步与反控制 INTERNET拥塞控制系统非线性动力学 复杂网络上的同步、控制、传播、搜索、社团结构 等…
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为国际分岔与混沌杂志 撰写复杂网络研究综述
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为IEEE电路与系统杂志 撰写复杂网络研究综述（封面文章）
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Crickets Synchronize their chirps
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Out of Tumultuous Applause, a Synchronized Clap

Self-organization in the concert-hall: the dynamics of rhythmic applause, Nature, 2001
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Biological Clock
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Electric currents through Josephson junctions oscillate as one
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Synchronization-based Laser

Also, astounding coherence of a laser beam comes from trillions of atoms pulsing in concert, all emitting photons of the same phase and frequency.
N.Wiener,Nonlinear Problems in Random Theory, MIT Press, Cambridge, MA,1958 N.Wiener, Cybernetics, MIT Press, Cambridge, MA, 1st Edition, 1948, 2nd Edition, 1961.
In 1960s, Arthur Winfree, a theoretical biologist began to study coupled oscillators

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Fireflies Synchronize their Flashes



The blinking of fireflies is one behavior that Winfree studied. As night falls on the jungles of Southeast Asia, fireflies begin to flicker, each following its own rhythm. But over the next hour or so, pockets of synchrony emerge and grow. Thousands of fireflies clustered around individual trees eventually flash as one, switching on and off every second or two to create a stunning entomological light show. How does such synchrony come about? In this case, each firefly has its own cycle of flashes, but that rhythm can be reset when the fly sees a flash from a neighbour. Pairs of flies become synchronized in this way, and the effect gradually spreads until large groups are linked. In general, oscillating units communicate by exchanging signals that prompt other units to alter their timing. Synchronization occurs if these „coupling‟ signals are influential enough to overcome the initial variation in individual frequencies. “Below a threshold, anarchy prevails; above it, there is a collective rhythm,”--- Winfree

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1. Synchronization: All together now
Synchronization is one of the most pervasive phenomena in the Universe.
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Synchronization of Clocks




The study of synchronous systems cuts across the disciplines of modern science. But the underlying phenomenon was first documented over three centuries ago. In 1665, Dutch physicist Christiaan Huygens lay ill in bed, watching the motions of two pendulum clocks he had built. To his surprise, he detected an “odd kind of sympathy” between the clocks: regardless of their initial state, the two pendulums soon adopted the same rhythm, one moving left as the other swung right. Elated, Huygens announced his finding at a special session of the Royal Society of London, attributing this synchrony to tiny forces transmitted between the clocks by the wooden beam from which they were suspended.