Discrete Dynamics in Nature and Society
Volume 2010 (2010), Article ID 905102, 10 pages
doi:10.1155/2010/905102
Research Article

Dynamic Properties of Coupled Maps

Chunrui Zhang1 and Huifeng Zheng2

1Department of Mathematics, Northeast Forestry University, Harbin 150040, China
2Department of Electrical and Computer Engineering, Pratt School of Engineering, Duke University, Durham, NC 27708, USA

Received 24 March 2010; Revised 16 July 2010; Accepted 8 August 2010

Academic Editor: Elena Braverman

Copyright © 2010 Chunrui Zhang and Huifeng Zheng. 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

Dynamic properties are investigated in the coupled system of three maps with symmetric nearest neighbor coupling and periodic boundary conditions. The dynamics of the system is controlled by certain coupling parameters. We show that, for some values of the parameters, the system exhibits nontrivial collective behavior, such as multiple bifurcations, and chaos. We give computer simulations to support the theoretical predictions.