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Stability and bifurcation analysis of a discrete predator-prey model with nonmonotonic functional response. (English) Zbl 1215.92063
Summary: The paper studies the dynamical behavior of a discrete predator-prey system with nonmonotonic functional response. The local stability of equilibria of the model is obtained. The model undergoes flip bifurcations and Hopf bifurcations by using the center manifold theorem and bifurcation theory. Numerical simulations not only illustrate our results, but also exhibit the complex dynamical behavior of the model, such as the period-doubling bifurcation in periods 2, 4 and 8, and quasi-periodic orbits and chaotic sets. The most interesting aspect is choosing the same parameters and the initial value of the model; then we vary the parameter $K$, and obtain series bifurcations, such as flip bifurcations and Hopf bifurcations.
##### MSC:
 92D40 Ecology 37N25 Dynamical systems in biology 39A28 Bifurcation theory (difference equations) 65C20 Models (numerical methods) 39A60 Applications of difference equations