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International Journal of Mathematics and Mathematical Sciences
Volume 2003, Issue 45, Pages 2887-2896
http://dx.doi.org/10.1155/S0161171203111234

On circle map coupled map lattice

1Mathematics Department, Faculty of Science, Mansoura University, Mansoura 35516, Egypt
2Department of Mathematics and Computer Since, Faculty of Science, United Arab Emirates University, Al-Ain P.O. Box 17551, United Arab Emirates

Received 27 November 2001

Copyright © 2003 Hindawi Publishing Corporation. 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

The circle map in one and two dimensions is studied. Both its stability and synchronization, using a bounded control and persistence, are discussed. This work is expected to be applicable in ecology where spatial effects are known to be important. Also, it will be relevant to systems where delay effects are not negligible.