Bifurcation analysis and chaos control in a host-parasitoid model. (English) Zbl 1383.92066

Din, Qamar; Saeed, Umer

Math. Methods Appl. Sci. 40, No. 14, 5391-5406 (2017).

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

Keywords:

host-parasitoid model; stability analysis; Neimark-Sacker bifurcation; chaos control