Rich dynamics of a discrete-time prey-predator model

Abstract

. A newly-disclosed non-standard finite difference method has been used to discretize a prey-predator model to investigate the critical normal form coefficients of bifurcations for both one-parameter and two-parameter bifurcations. The discrete-time prey-predator model exhibits variety of local bifurcations such as period-doubling, Neimark-Sacker, and strong resonances. Critical normal form coefficients are determined to reveal dynamical scenario corresponding to each bifurcation point bifurcation. We also investigates the complex dynamics of the model numerically using by M ATLAB package M ATCONT M based on numerical continuation technique.