The dynamical behavior of the predator-prey system is influenced effectively due to the mutual interaction of parasites. Regulations are imposed on biodiversity due to such type of interaction. With implementation of nonlinear saturated incidence rate and piecewise constant argument method of differential equations, a three-dimensional discrete-time model of prey-predator-parasite type is studied. The existence of equilibria and the local asymptotic stability of these steady states are investigated. Moreover, explicit criteria for a Neimark-Sacker bifurcation and a period-doubling bifurcation are implemented at positive equilibrium point of the discrete-time model. Chaos control is discussed through implementation of a hybrid control technique based on both parameter perturbation and a state feedback strategy. At the end, some numerical simulations are provided to illustrate our theoretical discussion.

In this article, a modification is proposed for the classical Nicholson–Bailey model. It is assumed that the modified model follows all axioms of Nicholson–Bailey model except that in every generation a fraction of the hosts have a safe refuge from attack of parasitoids. It is investigated that under this assumption the modified model has stable coexistence. Furthermore, Neimark–Sacker bifurcation is interrogated at positive steady-state of modified model by implementing the normal forms theory of bifurcation. Chaos control methods based on perturbation of parameter and state feedback strategy are implemented to escape the trajectories from bifurcating and chaotic behavior. Furthermore, numerical simulations are carried out for illustration of theoretical discussion. Finally, all theoretical discussion is illustrated by taking into account real observed field data of host–parasitoid interaction.

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In this paper, we study the dynamic of the predator–prey model based on mutual interference and its effects on searching efficiency. The parametric conditions, existence, and stability for trivial and boundary equilibrium points are studied. Also, it has shown that by applying the center manifold theorem and bifurcation theory, system undergoes Neimark–Sacker bifurcation across the neighborhood of a positive fixed point. Moreover, due to the bifurcation and chaos which objectively exist in a system, three chaos control strategies are designed and used. Moreover, to validate our theoretical and analytical discussions, numerical simulations are applied to show complex and chaotic behavior. Finally, theoretical discussions are validated with experimental field data.