Intermittent behaviors in weakly coupled map lattices

Tiexiang Li Southeast University Wen-Wei Lin National Chiao Tung University Yiqian Wang Nanjing University Shing-Tung Yau Harvard University

Dynamical Systems mathscidoc:1711.11001

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.
weakly-coupled map lattices,piecewise-expanding,intermittent,full Lebesgue measure,chaos
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@inproceedings{tiexiangintermittent,
  title={Intermittent behaviors in weakly coupled map lattices},
  author={Tiexiang Li, Wen-Wei Lin, Yiqian Wang, and Shing-Tung Yau},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20171109154403689071854},
}
Tiexiang Li, Wen-Wei Lin, Yiqian Wang, and Shing-Tung Yau. Intermittent behaviors in weakly coupled map lattices. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20171109154403689071854.
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