Covering relations for coupled map networks

TL;DR

This paper develops a general method using covering relations to estimate the topological entropy of coupled map networks over arbitrary graphs, without requiring hyperbolicity or linearity assumptions.

Contribution

It introduces a novel approach to estimate topological entropy in coupled map networks using covering relations, applicable to arbitrary finite graphs without hyperbolicity constraints.

Findings

Provides a lower bound for topological entropy of perturbed networks

Applies to networks with arbitrary finite graph structures

Does not assume hyperbolic local dynamics or linear coupling

Abstract

Following [6,12], we study coupled map networks over arbitrary finite graphs. An estimate from below for a topological entropy of a perturbed coupled map network via a topological entropy of an unperturbed network by making use of the covering relations for coupled map networks is obtained. The result is quite general, particularly no assumptions on hyperbolicity of a local dynamics or linearity of coupling are made.