Predator–prey dynamics in autonomous and nonautonomous settings: Impacts of anti-predator behavior, refuge, and additional food

Predator–prey interactions, shaped by anti-predator behaviors, refuge use, and resource availability, drive ecological dynamics and species evolution. This study presents autonomous and nonautonomous models to examine the effects of prey defense mechanisms and external food sources for predator populations. The autonomous model focuses on constant scenarios, while the nonautonomous model accounts for seasonal variations. Numerical results reveal the intricate roles of prey anti-predator behavior, refuge capacity, and external food sources in driving population dynamics. We identify parameter thresholds critical to the survival of middle predators, uncovering novel bistability phenomenon and multistability scenarios characterized by oscillatory coexistence and predator-free steady states. Saddle–node and homoclinic bifurcations illustrate the sensitivity of the system to minor changes in the parameter values, highlighting regime shifts between predator-dominated and predator-free states. Additionally, we observe “bubbling” phenomenon linked to reduced prey consumption rates by middle predators, further elucidating the system’s complexity. Seasonal perturbations of the parameters yield diverse behaviors, including periodic oscillation, bursting, and chaotic dynamics. Notably, chaotic dynamics emerge when refuge coefficients are varied, which is confirmed by a positive Lyapunov exponent. These findings emphasize the destabilizing impact of seasonal forcing, which can lead to the decline of middle predator population. Our results provide critical insights into the stability and resilience of food web interactions, offering valuable guidance for conservation strategies and ecosystem management under fluctuating environmental conditions.