Neimark–Sacker bifurcation and period-doubling bifurcation for a discretized fractional-order predator-prey system with Holling type II functional response

In this study, we examine the dynamical behaviors of the discrete form of a fractional-order predator-prey model with a Holling type II functional response. Specifically, we analyze the stability of its fixed points and the potential for various bifurcations by employing stability analysis methods and bifurcation theory. We explicitly show that, under specific parameter conditions, the system undergoes both a Neimark–Sacker bifurcation and a period-doubling bifurcation. Finally, several numerical simulations are performed to verify the analytical results derived earlier.