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Intermittent Behaviors in Coupled Piecewise Expanding Map Lattices

Year:    2021

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

Analysis in Theory and Applications, Vol. 37 (2021), Iss. 4 : pp. 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 xi(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, limn|x1(n)x2(n)|=0for   |c12|<14 and intermittent behaviors occur for |c12|>14, where 0c1 is the coupling.

Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/ata.OA-2020-0020

Analysis in Theory and Applications, Vol. 37 (2021), Iss. 4 : pp. 481–519

Published online:    2021-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    39

Keywords:    Synchronization pseudo synchronization phase transition Coupled map Lattices piecewise expanding map.

Author Details

Tiexiang Li Email

Wen-Wei Lin Email

Yiqian Wang Email

Shing-Tung Yau Email