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Volume 37, Issue 4
Intermittent Behaviors in Coupled Piecewise Expanding Map Lattices

Tiexiang Li, Wen-Wei Lin, Yiqian Wang & Shing-Tung Yau

Anal. Theory Appl., 37 (2021), pp. 481-519.

Published online: 2021-11

[An open-access article; the PDF is free to any online user.]

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  • Abstract

In this paper, we propose a new method to study intermittent behaviors of coupled piecewise-expanding map lattices. We show that the successive transition between ordered and disordered phases occurs for almost every orbit when the coupling is small. That is,

ata1.JPG

where $x_i(n)$ correspond to the coordinates of $m$ nodes at the iterative step $n$. Moreover, when the uncoupled system is generated by the tent map and the lattice consists of two nodes, we prove a phase transition occurs between synchronization and intermittent behaviors. That is, $$\lim_{n\rightarrow \infty}| x_1(n)-x_2(n)|=0\quad\text{for }\ \ \Big|c-\frac12\Big|<\frac14$$ and intermittent behaviors occur for $|c-\frac12|>\frac14$, where $0\le c\le 1$ is the coupling.

  • AMS Subject Headings

37D20, 37A25

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{ATA-37-481, author = {Li , TiexiangLin , Wen-WeiWang , Yiqian and Yau , Shing-Tung}, title = {Intermittent Behaviors in Coupled Piecewise Expanding Map Lattices}, journal = {Analysis in Theory and Applications}, year = {2021}, volume = {37}, number = {4}, pages = {481--519}, abstract = {

In this paper, we propose a new method to study intermittent behaviors of coupled piecewise-expanding map lattices. We show that the successive transition between ordered and disordered phases occurs for almost every orbit when the coupling is small. That is,

ata1.JPG

where $x_i(n)$ correspond to the coordinates of $m$ nodes at the iterative step $n$. Moreover, when the uncoupled system is generated by the tent map and the lattice consists of two nodes, we prove a phase transition occurs between synchronization and intermittent behaviors. That is, $$\lim_{n\rightarrow \infty}| x_1(n)-x_2(n)|=0\quad\text{for }\ \ \Big|c-\frac12\Big|<\frac14$$ and intermittent behaviors occur for $|c-\frac12|>\frac14$, where $0\le c\le 1$ is the coupling.

}, issn = {1573-8175}, doi = {https://doi.org/10.4208/ata.OA-2020-0020}, url = {http://global-sci.org/intro/article_detail/ata/19961.html} }
TY - JOUR T1 - Intermittent Behaviors in Coupled Piecewise Expanding Map Lattices AU - Li , Tiexiang AU - Lin , Wen-Wei AU - Wang , Yiqian AU - Yau , Shing-Tung JO - Analysis in Theory and Applications VL - 4 SP - 481 EP - 519 PY - 2021 DA - 2021/11 SN - 37 DO - http://doi.org/10.4208/ata.OA-2020-0020 UR - https://global-sci.org/intro/article_detail/ata/19961.html KW - Synchronization, pseudo synchronization, phase transition, Coupled map Lattices, piecewise expanding map. AB -

In this paper, we propose a new method to study intermittent behaviors of coupled piecewise-expanding map lattices. We show that the successive transition between ordered and disordered phases occurs for almost every orbit when the coupling is small. That is,

ata1.JPG

where $x_i(n)$ correspond to the coordinates of $m$ nodes at the iterative step $n$. Moreover, when the uncoupled system is generated by the tent map and the lattice consists of two nodes, we prove a phase transition occurs between synchronization and intermittent behaviors. That is, $$\lim_{n\rightarrow \infty}| x_1(n)-x_2(n)|=0\quad\text{for }\ \ \Big|c-\frac12\Big|<\frac14$$ and intermittent behaviors occur for $|c-\frac12|>\frac14$, where $0\le c\le 1$ is the coupling.

Tiexiang Li, Wen-Wei Lin, Yiqian Wang & Shing-Tung Yau. (1970). Intermittent Behaviors in Coupled Piecewise Expanding Map Lattices. Analysis in Theory and Applications. 37 (4). 481-519. doi:10.4208/ata.OA-2020-0020
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