U.S. Naval Research Laboratory, Washington, District of Columbia 20375, USA.
Chaos. 2015 Sep;25(9):097611. doi: 10.1063/1.4917383.
We review some of the history and early work in the area of synchronization in chaotic systems. We start with our own discovery of the phenomenon, but go on to establish the historical timeline of this topic back to the earliest known paper. The topic of synchronization of chaotic systems has always been intriguing, since chaotic systems are known to resist synchronization because of their positive Lyapunov exponents. The convergence of the two systems to identical trajectories is a surprise. We show how people originally thought about this process and how the concept of synchronization changed over the years to a more geometric view using synchronization manifolds. We also show that building synchronizing systems leads naturally to engineering more complex systems whose constituents are chaotic, but which can be tuned to output various chaotic signals. We finally end up at a topic that is still in very active exploration today and that is synchronization of dynamical systems in networks of oscillators.
我们回顾了混沌系统同步领域的一些历史和早期工作。我们从自己对这一现象的发现开始，但追溯到最早已知的论文，建立了这个主题的历史时间表。混沌系统的同步一直是一个有趣的话题，因为由于它们的正 Lyapunov 指数，混沌系统被认为难以同步。两个系统收敛到相同的轨迹是一个惊喜。我们展示了人们最初是如何思考这个过程的，以及随着时间的推移，同步流形的使用如何使这个概念从更几何的角度发生了变化。我们还表明，构建同步系统自然会导致构建更复杂的系统，这些系统的组成部分是混沌的，但可以调整输出各种混沌信号。最后，我们讨论了一个至今仍在积极探索的话题，即振荡器网络中的动力系统同步。
