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Bifurcation and chaos in a host-parasitoid model with a lower bound for the host. (English) Zbl 1445.37065
Summary: In this paper, a discrete-time biological model and its dynamical behaviors are studied in detail. The existence and stability of the equilibria of the model are qualitatively discussed. More precisely, the conditions for the existence of a flip bifurcation and a Neimark-Sacker bifurcation are derived by using the center manifold theorem and bifurcation theory. Numerical simulations are presented not only to validate our results with the theoretical analysis, but also to exhibit the complex dynamical behaviors. We also analyze the dynamic characteristics of the system in a two-dimensional parameter space. Numerical results indicate that we can more clearly and directly observe the chaotic phenomenon, period-doubling and period-adding, and the optimal parameters matching interval can also be found easily.

MSC:
37N25 Dynamical systems in biology
92D25 Population dynamics (general)
92D30 Epidemiology
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