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In this study, the dynamical behaviors of a discrete time eco-epidemiological system are discussed. The local stability, bifurcation and chaos are obtained. Moreover, the global asymptotical stability of this system is explored by an iteration scheme. The numerical simulations illustrate the theoretical results and exhibit the complex dynamical behaviors such as flip bifurcation, Hopf bifurcation and chaotic dynamical behaviors. Our main results provide an efficient method to analyze the global asymptotical stability for general three dimensional discrete systems. [ABSTRACT FROM AUTHOR]

Abstract: The paper discusses the dynamical behaviors of a discrete-time SIR epidemic model. The local stability of the disease-free equilibrium and endemic equilibrium is obtained. It is shown that the model undergoes flip bifurcation and Hopf bifurcation by using center manifold theorem and bifurcation theory. Numerical simulations not only illustrate our results, but also exhibit the complex dynamical behaviors, such as the period-doubling bifurcation in period-2, 4, 8, quasi-periodic orbits and the chaotic sets. These results reveal far richer dynamical behaviors of the discrete epidemic model compared with the continuous epidemic models although the discrete epidemic model is easy. [Copyright &y& Elsevier]