1997/04/01 by Reggie Brown, Nikolai F. Rulkov · 59 citations
Computer Science · Mathematics · Physics and Astronomy · #Applied mathematics #Chaos control and synchronization #Chaotic #Chaotic systems #Computer science #Control (management) #Control theory (sociology) #Discrete time and continuous time #Dynamical systems theory #Invariant (physics) #Mathematics #Nonlinear Dynamics and Pattern Formation #Physics #Quantum chaos and dynamical systems #Stability (learning theory) #Stability criterion #Statistical physics #Synchronization (alternating current) #Synchronization of chaos #Topology (electrical circuits) #Trajectory #chao-dyn #nlin.CD
paper · pdf · doi:10.1063/1.166213
published in Chaos An Interdisciplinary Journal of Nonlinear Science 7(3), 395-413 (American Institute of Physics) · RevTex, 22 pages, 5 tables, and 18 eps figures, submitted for publication
arxiv created 1997/04/01 · openalex publication_date 1997/09/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.