Bifurcation results and chaos in a two-dimensional predator-prey model incorporating Holling-type response function on the predator

This study presents a novel two-dimensional discrete-time predator-prey model incorporating a Holling-type response function on the predator. The focus lies on identifying stationary points and investigating multiple bifurcations around the positive fixed point, taking into account their biological significance. Notably, our analysis of bifurcations at the interior fixed point unveils a range of generic bifurcations, including one-parameter and two-parameter bifurcations, as well as period-doubling, Neimark-Sacker, and strong resonance bifurcations. We establish non-degeneracy conditions and calculate coefficients of critical normal form to deepen our understanding of the computed bifurcations. To validate our analytical results, we employ the MatContM package in MATLAB, which showcases complex dynamics up to the fourth iteration. Remarkably, the remarkable correlation between numerical simulations and analytical findings serves as compelling evidence for the robustness of our presented analytical results. This work contributes novel insights into the dynamics of predator-prey models and highlights the unique aspects of bifurcation phenomena in this particular context.