Hierarchy and stability of partially synchronous oscillations of diffusively coupled dynamical systems

作     者：Vladimir N. Belykh Igor V. Belykh Martin Hasler 

作者机构：Advanced School of General and Applied Physics Nizhny Novgorod University 23 Gagarin Avenue Nizhny Novgorod 603600 Russia Department of Differential Equations Institute for Applied Mathematics and Cybernetics Nizhny Novgorod University 10 Ul’yanov Street Nizhny Novgorod 603 005 Russia Department of Electrical Engineering Swiss Federal Institute of Technology Lausanne (EPFL) CH-1015 Lausanne Switzerland 

出 版 物：《Physical Review E》 (物理学评论E辑：统计、非线性和软体物理学)

年 卷 期：2000年第62卷第5期

页      面：6332-6332页

核心收录：

学科分类：07[理学] 070203[理学-原子与分子物理] 0702[理学-物理学] 

主　　题：Chaos theory 

摘      要：The paper presents a qualitative analysis of an array of diffusively coupled identical continuous time dynamical systems. The effects of full, partial, antiphase, and in-phase–antiphase chaotic synchronizations are investigated via the linear invariant manifolds of the corresponding differential equations. The existence of various invariant manifolds, a self-similar behavior, and a hierarchy and embedding of the manifolds of the coupled system are discovered. Sufficient conditions for the stability of the invariant manifolds are obtained via the method of Lyapunov functions. Conditions under which full global synchronization cannot be achieved even for the largest coupling constant are defined. The general rigorous results are illustrated through examples of coupled Lorenz-like and Rössler systems.