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

TL;DR

This paper identifies a critical lattice size limit for maintaining synchronized chaotic states in 1-D and 2-D diffusively coupled map lattices, extending previous results to arbitrary neighbor coupling.

Contribution

It generalizes the critical size limit for synchronization stability to P-neighbor coupling in both 1-D and 2-D lattices, supported by analytical and numerical analysis.

Findings

Existence of a critical lattice size for synchronization stability.

Analytical derivation of the size limit for arbitrary neighbor coupling.

Numerical confirmation of the analytical results.

Abstract

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.