Bifurcation Analysis of a Discrete-Time Prey-Predator Model: Theory and Numerical Continuation

This paper presents a comprehensive analysis of the bifurcation behavior of a two-dimensional predator-prey model described by a system of nonlinear difference equations. The study investigates the behavior of the system under different parameter regimes using both analytical and numerical techniques. Analytically, we employ a perturbation method to expand the system’s equations in a power series about the bifurcation point. This allows us to identify the types and scenarios of bifurcations that occur in the system, including period doubling, Neimark-Sacker, and strong resonance bifurcations. Numerical continuation methods implemented in MatcontM are used to validate the analytical results and gain further insights into the bifurcation structures.