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Zbl 1215.92063
Hu, Zengyun; Teng, Zhidong; Zhang, Long
Stability and bifurcation analysis of a discrete predator-prey model with nonmonotonic functional response. (English)
[J] Nonlinear Anal., Real World Appl. 12, No. 4, 2356-2377 (2011). ISSN 1468-1218

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 2000:: *92D40 Ecology
37N25 Dynamical systems in biology
39A28
65C20 Models (numerical methods)
39A60

Keywords: discrete model; flip bifurcation; Hopf bifurcation; center manifold theorem; numerical simulation

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Zentralblatt MATH Berlin [Germany]