Abd-Elalim A. Elsadany Computational Ecology and Software 2220-721X 2012 2 124-139 06/2012 International Academy of Ecology and Environmental Sciences discrete food chain discrete Hopf bifurcation strange attractor Lyapunov exponents 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. DOI 10.0000/issn-2220-721x-compuecol-2012-v2-0010 http://www.iaees.org/publications/journals/ces/articles/2012-2(2)/dynamical-complexities-in-a-discrete-time-food-chain.pdf