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,
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 |c−12|<14 and intermittent behaviors occur for |c−12|>14, where 0≤c≤1 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