Strong Allee Effect and Evolutionary Dynamics in a Single-Species Ricker Population Model

Abstract

In this paper, a discrete-time Ricker population model with the strong Allee effect is proposed, and its complex dynamic behavior is analyzed. First, the existence and asymptotic stability of the unique positive equilibrium are studied. Second, Neimark–Sacker and period-doubling bifurcations of this discrete model were carried out, and corresponding bifurcation conditions were obtained. Third, the pole placement method and the hybrid control strategy have been used to control the chaos produced by these bifurcations. Finally, we use MATLAB software to carry out some numerical simulations to analyze the rich dynamics of the system as well as to verify our theoretical results.