Open AccessDependence of Initial Value on Pattern Formation for a Logistic Coupled Map Lattice
Author(s) -
Li Xu,
Guang Zhang,
Haoyue Cui
Publication year - 2016
Publication title -
plos one
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.99
H-Index - 332
ISSN - 1932-6203
DOI - 10.1371/journal.pone.0158591
Subject(s) - eigenvalues and eigenvectors , logistic map , pattern formation , statistical physics , coupled map lattice , lattice (music) , initial value problem , mathematics , physics , statistics , computer science , mathematical analysis , biology , control theory (sociology) , artificial intelligence , quantum mechanics , control (management) , synchronization of chaos , chaotic , acoustics , genetics
The logistic coupled map lattices (LCML) have been widely investigated as well as their pattern dynamics. The patterns formation may depend on not only fluctuations of system parameters, but variation of the initial conditions. However, the mathematical discussion is quite few for the effect of initial values so far. The present paper is concerned with the pattern formation for a two-dimensional Logistic coupled map lattice, where any initial value can be linear expressed by corresponding eigenvectors, and patterns formation can be determined by selecting the corresponding eigenvectors. A set of simulations are conducted whose results demonstrate the fact. The method utilized in the present paper could be applied to other discrete systems as well.