Brown Reggie, Rulkov Nikolai F.
Institute for Nonlinear Science, University of California, San Diego, La Jolla, California 92093-0402.
Chaos. 1997 Sep;7(3):395-413. doi: 10.1063/1.166213.
We examine synchronization of identical chaotic systems coupled in a drive/response manner. A rigorous criterion is presented which, if satisfied, guarantees that synchronization to the driving trajectory is linearly stable to perturbations. An easy to use approximate criterion for estimating linear stability is also presented. One major advantage of these criteria is that, for simple systems, many of the calculations needed to implement them can be performed analytically. Geometrical interpretations of the criterion are discussed, as well as how they may be used to investigate synchronization between mutual coupled systems and the stability of invariant manifolds within a dynamical system. Finally, the relationship between our criterion and results from control theory are discussed. Analytical and numerical results from tests of these criteria on four different dynamical systems are presented. (c) 1997 American Institute of Physics.
我们研究以驱动/响应方式耦合的相同混沌系统的同步。提出了一个严格的判据，若该判据得到满足，则可保证对驱动轨迹的同步对于微扰是线性稳定的。还给出了一个易于使用的用于估计线性稳定性的近似判据。这些判据的一个主要优点是，对于简单系统，实施它们所需的许多计算都可以解析地进行。讨论了该判据的几何解释，以及如何用它们来研究相互耦合系统之间的同步和动力系统中不变流形的稳定性。最后，讨论了我们的判据与控制理论结果之间的关系。给出了在四个不同动力系统上对这些判据进行测试的解析和数值结果。（c）1997美国物理研究所。
