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Bifurcation analysis and chaos control in a host-parasitoid model. (English) Zbl 1383.92066
Summary: We investigate the qualitative behavior of a host-parasitoid model with a strong Allee effect on the host. More precisely, we discuss the boundedness, existence and uniqueness of positive equilibrium, local asymptotic stability of positive equilibrium and existence of Neimark-Sacker bifurcation for the given system by using bifurcation theory. In order to control Neimark-Sacker bifurcation, we apply pole-placement technique that is a modification of OGY method. Moreover, the hybrid control methodology is implemented in order to control Neimark-Sacker bifurcation. Numerical simulations are provided to illustrate theoretical discussion.

MSC:
92D25 Population dynamics (general)
39A30 Stability theory for difference equations
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