Intermittent behaviors in weakly coupled map lattices

TL;DR

This paper investigates intermittent behaviors in weakly coupled map lattices, demonstrating phase transitions between order and disorder for almost all orbits, applicable to two-node and multi-node systems.

Contribution

It proves phase transition phenomena in coupled map lattices with weak coupling, extending results to multi-node systems and different types of maps.

Findings

Successive phase transitions between ordered and disordered states.

Almost every orbit exhibits both synchronized and desynchronized phases.

Results apply to both piecewise-expanding and tent-map lattices.

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 $\liminf_{n\rightarrow \infty}| x_1(n)-x_2(n)|=0$ and $\limsup_{n\rightarrow \infty}| x_1(n)-x_2(n)|\ge c_0>0$, where $x_1(n), x_2(n)$ 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.