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

2025/07/19 by Zhang, Junke, Wang, Yiqian
#37A05 #37A10 #Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.2507.14646

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.

Citations

• Does the brain behave like a (complex) network? I. Dynamics
• Multidimensional expanding maps with singularities: a pedestrian\n approach
• Transfer Operators for Coupled Analytic Maps
• Period-Doubling of Kink-Antikink Patterns, Quasiperiodicity in Antiferro-Like Structures and Spatial Intermittency in Coupled Logistic Lattice: Towards a Prelude of a "Field Theory of Chaos"

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