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This is a Quantitative Study study.

October 3, 2025

Intermittent synchronization in non-weakly coupled piecewise-linear expanding map lattice: A geometric-combinatorial approach

Key Points

The study demonstrates that intermittent synchronization can occur in coupled chaotic map lattices with a geometric-combinatorial approach.
A necessary and sufficient condition for unique invariant measures is established in two-node systems with piecewise-linear maps.
The findings extend previous understanding of dynamical behavior in weakly coupled scenarios, indicating broader applications.
This method provides new insights into complex systems, potentially enhancing studies in nonlinear dynamics.

Abstract

Coupled (chaotic) map lattices (CMLs) characterize the collective dynamics of a spatially distributed system whose local units are linked either locally or globally. Previous research on the dynamical behavior of CMLs, based primarily on the Perron–Frobenius operator framework, has focused mainly on the weakly coupled case. In this paper, we develop a novel geometric-combinatorial method to study the dynamical behavior of CMLs beyond the weak-coupling regime, specifically a two-node system with identical piecewise-linear expanding maps. We derive a necessary and sufficient condition for two facts: the uniqueness of the absolutely continuous invariant measures and the occurrence of intermittent synchronization—i.e., almost every orbit enters and leaves an arbitrarily small neighborhood of the diagonal infinitely often.

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