Intermittent Behaviors in Coupled Piecewise Expanding Map Lattices  

作　　者：Tiexiang Li Wen-Wei Lin Yiqian Wang Shing-Tung Yau 

机构地区：[1]Department of Mathematics,Southeast Univeristy,Nanjing,Jiangsu 211189,China [2]Nanjing Center for Applied Mathematics,Nanjing,Jiangsu 211135,China [3]Department of Mathematics,National Chiao Tung University,Hsinchu,300,Taiwan [4]Department of Mathematics,Nanjing University,Nanjing,Jiangsu 210093,China [5]Department of Mathematics,Harvard University,Boston,USA

出　　处：《Analysis in Theory and Applications》2021年第4期481-519,共39页分析理论与应用（英文刊）

基　　金：This work is supported by NSFC of China(Grants Nos.11031003,11271183,11971105 and 11771205)and Simons Foundation.

摘　　要：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,lim inf n→∞∑1≤i,j≤m|x_(i)(n)−x_(j)(n)|=0,lim sup n→∞∑1≤i,j≤m|x_(i)(n)−x_(j)(n)|≥c_(0)>0,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→∞|x_(1)(n)−x_(2)(n)|=0 for c−1/2<1/4 and intermittent behaviors occur for|c−1/2|>1/4,where 0≤c≤1 is the coupling.

关 键 词：SYNCHRONIZATION pseudo synchronization phase transition Coupled map Lattices piecewise expanding map 

分 类 号：O177.91[理学—数学]