Dynamics and bifurcations of a discrete‐time Lotka–Volterra model using nonstandard finite difference discretization method

Abstract

A newly disclosed nonstandard finite difference method has been used to discretize a Lotka–Volterra 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 a variety of local bifurcations such as period‐doubling, Neimark–Sacker, and strong resonances. Critical normal form coefficients are determined to reveal dynamical scenarios corresponding to each bifurcation point. We also investigate the complex dynamics of the model numerically by Matlab package using MatcotM based on numerical continuation technique. The numerical continuation validates the theoretical analysis, which is discussed from an ecological perspective.