Intermittent--synchronization in non-weakly coupled piecewise linear expanding map lattice: a geometric-combinatorics method

TL;DR

This paper introduces a geometric-combinatorics approach to analyze the dynamic behavior of non-weakly coupled chaotic map lattices, focusing on synchronization phenomena and invariant measures.

Contribution

It presents a novel method for studying non-weakly coupled CMLs, providing conditions for invariant measure uniqueness and intermittent synchronization.

Findings

Established necessary and sufficient conditions for ACIM uniqueness.

Identified criteria for the occurrence of intermittent synchronization.

Analyzed the dynamical behavior of two-node piecewise linear expanding map lattices.

Abstract

The coupled (chaotic) map lattices (CMLs) characterizes the collective dynamics of a spatially distributed system consisting of locally or globally coupled maps. The current research on the dynamic behavior of CMLs is based on the framework of the Perron-Frobenius operator and mainly focuses on weakly-coupled cases. In this paper, a novel geometric-combinatorics method for for non weakly-coupled CMLs is provided on the dynamical behavior of a two-node CMLs with identical piecewise linear expanding maps. We obtain a necessary-sufficient condition for the uniqueness of absolutely continuous invariant measure (ACIM) and for the occurrence of intermittent-synchronization, that is, almost each orbit enters and exits an arbitrarily small neighborhood of the diagonal for an infinite number of times.