Neimark-Sacker bifurcation and chaos control in discrete-time predator-prey model with parasites

In this paper, we discuss the qualitative behavior of a four-dimensional discrete-time predator-prey model with parasites. We investigate existence and uniqueness of positive steady state and find parametric conditions for local asymptotic stability of positive equilibrium point of given system. It is also proved that the system undergoes Neimark-Sacker bifurcation (NSB) at positive equilibrium point with the help of an explicit criterion for NSB. The system shows chaotic dynamics at increasing values of bifurcation parameter. Chaos control is also discussed through implementation of hybrid control strategy, which is based on feedback control methodology and parameter perturbation. Finally, numerical simulations are conducted to illustrate theoretical results.