Bifurcation and Stability Analysis of a Discrete Predator–Prey Model with Alternative Prey

Abstract

In this paper, we investigate the dynamics of a class of discrete predator–prey model with alternative prey. We prove the boundedness of the solution, the existence and local/global stability of equilibrium points of the model, and verify the existence of flip bifurcation and Neimark-Sacker bifurcation. In addition, we use the maximum Lyapunov exponent and isoperimetric diagrams to verify the existence of periodic structures namely Arnold tongue and the shrimp-shaped structures in bi-parameter spaces of a class of predator–prey model.