Stability of Synchronized Chaos in Coupled Dynamical Systems

Abstract

We consider the stability of synchronized chaos in coupled map lattices and in coupled ordinary differential equations. Applying the theory of Hermitian and positive semidefinite matrices we prove two results that give simple bounds on coupling strengths which ensure the stability of synchronized chaos. Previous results in this area involving particular coupling schemes (e.g. global coupling and nearest neighbor diffusive coupling) are included as special cases of the present work.

9 pages

Cited by in corpus (12)

• Cluster synchronization in networks of coupled non-identical dynamical systems
• Evolving networks with distance preferences
• General Stability Analysis of Synchronized Dynamics in Coupled Systems
• Amplitude death in complex networks induced by environment
• Synchronization of coupled nonidentical dynamical systems
• Chaos synchronization in long-range coupled map lattices
• Generalized Turing Patterns and Their Selective Realization in Spatiotemporal Systems
• Desynchronized wave patterns in synchronized chaotic regions of coupled map lattices
• Critical Lattice Size Limit for Synchronized Chaotic State in 1-D and 2-D Diffusively Coupled Map Lattices
• Scaling and synchronization in a ring of diffusively coupled nonlinear oscillators
• Desynchronization bifurcation of coupled nonlinear dynamical systems
• Synchronization in delayed discrete-time complex networks