Karima Mokni - Faculte Polydisciplinaire Khouribga, Sultan moulay Slimane University, BP: ۱۴۵ Khouribga principale, ۲۵۰۰۰, Kingdom of Morocco
Mohamed Ch-Chaoui - Faculte Polydisciplinaire Khouribga, Sultan moulay Slimane University, BP: ۱۴۵ Khouribga principale, ۲۵۰۰۰, Kingdom of Morocco
Rachid Fakhar - Faculte Polydisciplinaire Khouribga, Sultan moulay Slimane University, BP: ۱۴۵ Khouribga principale, ۲۵۰۰۰, Kingdom of Morocco

In this paper, we investigate a discrete-time prey-predator model. The system is formulated by using the piecewise constant argument method for differential equations and taking into account Holling type III. The existence and local behavior of equilibria are studied. We established that the system experienced both Neimark-Sacker and period-doubling bifurcations analytically by using bifurcation theory and the center manifold theorem. In order to control chaos and bifurcations, the state feedback method is implemented. Numerical simulations are also provided for the theoretical discussion.

difference equation, Asymptotic stability, Bifurcation analysis, Holling’s type ۳, chaos control