Multiple Codimension 2 Bifurcations in a Discrete‐Time Predator–Prey Model With Gompertz Growth of Prey and Holling Type III Functional Response

ABSTRACT In this paper, a discrete‐time predator–prey model with Holling type III functional response and Gompertz growth of prey proposed by Almatrafi et al. is investigated. Based on the bifurcation theory, the center manifold theorem, and the method of normal forms, we theoretically analyze the codimension 2 bifurcations of this system, including the generalized flip bifurcation and the 1:2, 1:3, and 1:4 strong resonance bifurcations. Moreover, we use numerical simulations to demonstrate our analysis. The bifurcation diagrams, numerical continuations, maximum Lyapunov exponents, and phase portraits are applied to illustrate the theoretical results and display some new dynamical phenomena. In addition, the two‐parameter space diagrams plotted in regions away from the critical values of the bifurcation parameters reveal the global dynamics of the system. This work verifies that this discrete system exhibits a variety of complex and rich dynamical properties.