Intermittent behaviors in weakly coupled 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 ${\mathrm{liminf}}_{n\to \infty }|x_1(n)-x_2(n)|=0$ and ${\mathrm{limsup}}_{n\to \infty }|x_1(n)-x_2(n)|\ge c_0>0$, 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.

33 pages, 4 figures

References in corpus (1)

• Phase transitions in a piecewise expanding coupled map lattice with linear nearest neighbour coupling