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Bifurcation analysis and chaos control in a discrete-time parasite-host model. (English) Zbl 1369.92089
Summary: A discrete-time parasite-host system with bifurcation is investigated in detail in this paper. The existence and stability of nonnegative fixed points are explored and the conditions for the existence of flip bifurcation and Neimark-Sacker bifurcation are derived by using the center manifold theorem and bifurcation theory. And we also prove the chaos in the sense of Marotto. The numerical simulations not only illustrate the consistence with the theoretical analysis, but also exhibit other complex dynamical behaviors, such as bifurcation diagrams, Maximum Lyapunov exponents, and phase portraits. More specifically, when the integral step size is chosen as a bifurcation parameter, this paper presents the finding of period orbits, attracting invariant cycles and chaotic attractors of the discrete-time parasite-host system. Specifically, we have stabilized the chaotic orbits at an unstable fixed point by using the feedback control method.

MSC:
92D25 Population dynamics (general)
92D30 Epidemiology
34K23 Complex (chaotic) behavior of solutions to functional-differential equations
34K18 Bifurcation theory of functional-differential equations
37G10 Bifurcations of singular points in dynamical systems
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