Intermittent behaviors in weakly coupled map lattices

2017/11/04 by Tiexiang Li, Wen‐Wei Lin, Li, Tiexiang +5
Computer Science · Physics and Astronomy · #37A25 #37C30 #37C40 #Chaos control and synchronization #Dynamical Systems (math.DS) #FOS: Mathematics #Nonlinear Dynamics and Pattern Formation #Quantum chaos and dynamical systems

paper · pdf · doi:10.48550/arxiv.1711.01457

openalex publication_date 2017/11/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we study intermittent behaviors of coupled piecewise-expanding map lattices with two nodes and a weak coupling. We show that the successive phase transition between ordered and disordered phases occurs for almost every orbit. That is, we prove \liminf_{n→ ∞}| x₁(n)-x₂(n)|=0 and \limsup_{n→ ∞}| x₁(n)-x₂(n)|≥ c₀>0, where x₁(n), x₂(n) correspond to the coordinates of two nodes at the iterative step n. We also prove the same conclusion for weakly coupled tent-map lattices with any multi-nodes.

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