Nonlinear dynamics in a discrete-time predator-prey system

Abstract

In this paper, the nonlinear dynamics of a two-dimensional discrete-time system of Leslie type 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 at the positive fixed point. For each bifurcation, normal form coefficients along with its scenario are investigated thoroughly. Besides, using numerical simulations, in addition to confirming the results of our analyses, more behaviors are extracted from the model, such as fractal structure, mode-locking structure, etc. Our results generate and improve some known results and show that the discrete model has richer dynamics than the continuous one.