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arXiv · 2507.14646

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

Junke Zhang·Yiqian Wang
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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.

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Junke Zhang, Yiqian Wang. 2025-07-19. Intermittent--synchronization in non-weakly coupled piecewise linear expanding map lattice: a geometric-combinatorics method. https://arxiv.org/abs/2507.14646

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