Discrete Dynamics in Nature and Society
Volume 2011 (2011), Article ID 174376, 16 pages
http://dx.doi.org/10.1155/2011/174376
Research Article

A Proof for the Existence of Chaos in Diffusively Coupled Map Lattices with Open Boundary Conditions

Li-Guo Yuan1,2 and Qi-Gui Yang1

1School of Mathematical Sciences, South China University of Technology, Guangzhou 510640, China
2Department of Applied Mathematics, South China Agricultural University, Guangzhou 510640, China

Received 2 July 2011; Accepted 13 September 2011

Academic Editor: Recai Kilic

Copyright © 2011 Li-Guo Yuan and Qi-Gui Yang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We first study how to make use of the Marotto theory to prove rigorously the existence of the Li-Yorke chaos in diffusively coupled map lattices with open boundary conditions (i.e., a high-dimensional discrete dynamical system). Then, the recent 0-1 test for chaos is applied to confirm our theoretical claim. In addition, we control the chaotic motions to a fixed point with delay feedback method. Numerical results support the theoretical analysis.