Discrete Bazykin’s Prey–Predator Model with Stability, Control and Bifurcation

Abstract

In this paper, we have studied stability, bifurcation analysis and hybrid control in a discrete Bazykin’s model. Specifically, we have examined periodic points, local behavior at fixed points and potential bifurcation analysis of the discrete Bazykin’s model. It is proved that no flip bifurcation occurs at trivial fixed point but Bazykin’s model undergoes Neimark–Sacker bifurcation at interior fixed point. Moreover, hybrid control strategy is utilized in order to control the Neimark–Sacker bifurcation. Finally, extensive numerical simulations are provided to verify theoretical results.