Complex dynamics of a nonlinear discrete predator–prey system with fear factor and harvesting effect

Abstract

In this paper, a class of discrete-time predator–prey system with fear factor and harvesting effect is proposed, and its complex dynamic behavior is analyzed. First, the existence and stability of equilibrium points of the discrete system are studied. Second, the critical value expressions of Neimark–Sacker bifurcation and flip bifurcation are obtained by bifurcation theory. Third, we control the bifurcation and chaos of the system by using feedback control strategies. The optimal harvesting strategy is obtained by using the Pontryagin maximum principle. Finally, we use MATLAB software to carry out some numerical simulations, which not only verify our theoretical results, but also analyze the rich dynamic behavior of the system.