Multiple Bifurcations and Dynamics of a Discrete Time Predator-Prey System with Group Defense and Non-Monotonic Functional Response

摘要

In this paper, using the forward Euler method, we present a discrete predator-prey model with group defense and non-monotonic functional response. We study the stability of fixed points and analyze the bifurcations phenomena. Using the ideas of center manifold theorem, bifurcation theory and normal form methods we prove that the system undergoes fold bifurcation, flip bifurcation, Neimark-Sacker bifurcation and codimension two (i.e. 1:1 resonance) bifurcation. At the same time, complex dynamics and chaotic behaviors are justified numerically via computing the maximum Lyapunov exponent. Furthermore, we show that for some parameter values the system exhibits the so-called "paradox of enrichment" phenomenon.