Critical Lattice Size Limit for Synchronized Chaotic State in 1-D and 2-D Diffusively Coupled Map Lattices

Details Critical Lattice Size Limit for Synchronized Chaotic State in 1-D and 2-D Diffusively Coupled Map Lattices Critical Lattice Size Limit for Synchronized Chaotic State in 1-D and 2-D Diffusively Coupled Map Lattices

2007-11-19

arxiv.org/abs/0711.2851v1

Physical Review E, v.76, 027202 (2007)

Nonlinear Sciences

Chaotic Dynamics

4 pages, 2 figures

Scientific paper

10.1103/PhysRevE.76.027202

We consider diffusively coupled map lattices with $P$ neighbors (where $P$ is arbitrary) and study the stability of synchronized state. We show that there exists a critical lattice size beyond which the synchronized state is unstable. This generalizes earlier results for nearest neighbor coupling. We confirm the analytical results by performing numerical simulations on coupled map lattices with logistic map at each node. The above analysis is also extended to 2-dimensional $P$-neighbor diffusively coupled map lattices.

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