The Effects of Fluctuating Carrying Capacity on the Dynamics of a Holling-Type III Predator–Prey Model

This study investigates the complex dynamics of a predator–prey system governed by the classical Lotka–Volterra model incorporating a Holling-type III. To capture environmental variability, the prey’s carrying capacity is modeled as a periodic function, introducing a time-dependent forcing into the system. The resulting nonautonomous system is transformed into an equivalent autonomous system by coupling it with an auxiliary oscillator. Through numerical continuation techniques and bifurcation analysis using MATCONT, we explore the emergence of rich dynamical behaviors, including Hopf and limit point cycle bifurcations, Neimark–Sacker and period-doubling bifurcations, and two different routes to chaos. The results reveal that fluctuations in the carrying capacity significantly influence the system’s long-term behavior, leading to differently-periodic and quasiperiodic solutions, bistability, and chaos via two routes: torus destruction and cascade of period-doublings. These findings provide new insights into the ecological implications of environmental forcing in predator–prey interactions.