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arXiv · 1711.01457

Intermittent behaviors in weakly coupled map lattices

Tiexiang Li·Wen-wei Lin·Yiqian Wang·Shing-Tung Yau
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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.

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Tiexiang Li, Wen-wei Lin, Yiqian Wang, Shing-Tung Yau. 2017-11-04. Intermittent behaviors in weakly coupled map lattices. https://arxiv.org/abs/1711.01457

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