Nonlinear dynamics in a discrete-time predator-prey system

Abstract

In this article, the nonlinear dynamics of a discrete-time predator-prey system with simplified Holling type IV functional response are reported. Possible codimension-two bifurcations (1:2, 1:3 and 1:4 strong resonances) are investigated under variation of two parameters for certain critical values. For each bifurcation, normal form coefficients along with its scenario are investigated thoroughly. Besides, the numerical simulations have been done, in addition to supporting the analytical findings, more behaviors are extracted from the model, such as fractal structures, mode-locking structures, etc. Our results generate and improve some known results and show that the discrete model has richer dynamics than the continuous one.