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Computational Ecology and Software, 2012, 2(2): 124-139
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Article

Dynamical complexities in a discrete-time food chain

Abd-Elalim A. Elsadany
Department of Basic Science, Faculty of Computers and Informatics, Ismailia, Suez Canal University, Egypt

Received 13 March 2012;Accepted 20 April 2012;Published online 1 June 2012
IAEES

Abstract
In this paper, a discrete-time food chain characterized by three species is modeled by a system of three nonlinear difference equations. The existence and local stability of the equilibrium points of the discrete dynamical system are analyzed. It is shown that for some parameter values the interior equilibrium point loses its stability through a discrete Hopf bifurcation. Basic properties of the discrete system are analyzed by means of phase portraits, bifurcation diagrams and Lyapunov exponents. We have varied the result through numerical calculation.

Keywords discrete food chain;discrete Hopf bifurcation;strange attractor;Lyapunov exponents.



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