Intermittent--synchronization in non-weakly coupled piecewise linear expanding map lattice: a geometric-combinatorics method
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.
Cite
@article{arxiv.2507.14646,
title = {Intermittent--synchronization in non-weakly coupled piecewise linear expanding map lattice: a geometric-combinatorics method},
author = {Junke Zhang and Yiqian Wang},
journal= {arXiv preprint arXiv:2507.14646},
year = {2025}
}
Comments
21 pages,20 figures