Desynchronized wave patterns in synchronized chaotic regions of coupled map lattices

Abstract

We analyze the size limits of coupled map lattices with diffusive coupling at the crossover of low-dimensional to high-dimensional chaos. We investigate the existence of standing-wave-type periodic patterns, within the low-dimensional limit, in addition to the stable synchronous chaotic states depending upon the initial conditions. Further, we bring out a controlling mechanism to explain the emergence of standing-wave patterns in the coupled map lattices. Finally, we give an analytic expression in terms of the unstable periodic orbits of the isolated map to represent the standing-wave patterns.

5 pages, 3 figures, 2 tables (final version)

References in corpus (5)

• Stability of Synchronized Chaos in Coupled Dynamical Systems
• General Stability Analysis of Synchronized Dynamics in Coupled Systems
• Desynchronization waves and localized instabilities in oscillator arrays
• Local dimension and finite time prediction in spatiotemporal chaotic systems
• Estimation of System Parameters in Discrete Dynamical Systems from Time Series

Cited by in corpus (4)

• Critical parameters of the synchronisation's stability for coupled maps in regular graphs
• Low dimensional behavior in three-dimensional 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