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Computational Ecology and Software, 2012, 2(3): 169-180
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Article

Chaos and bifurcation of a nonlinear discrete prey-predator system

Abd-Elalim A. Elsadany 1, H. A. EL-Metwally2,3, E. M. Elabbasy2, H. N. Agiza2
1Department of Basic Science, Faculty of Computers and Informatics, 41522, Ismailia, Suez Canal University, Egypt
2Department of Mathematics, Faculty of Science, 35516, Mansoura University, Egypt
3Department of Mathematics, Rabigh College of Science and Art, King Abdulaziz University, P.O. Box 344, Rabigh 21911, Saudi Arabia

Received 12 May 2012;Accepted 20 June 2012;Published online 1 September 2012
IAEES

Abstract
The discrete-time Prey-predator system obtained by two dimensional map was studied in present study. The fixed points and their stability were analyzed. Bifurcation diagram has been obtained for selected range of different parameters. As some parameters varied, the model exhibited chaos as a long time behavior. Lyapunov exponents and fractal dimension of the chaotic attractor of our map were also calculated. Complex dynamics such as cycles and chaos were observed.

Keywords prey-predator system;chaotic behavior;Lyapunov exponents;fractal dimension.


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