Dynamical behaviors of autonomous and nonautonomous models of generalist predator–prey system with fear, mutual interference and nonlinear harvesting

In this study, we explore a predator–prey model to evaluate the impacts of fear, mutual interference, and harvesting, as these factors play crucial roles in modifying population dynamics, trophic cascades, and species interactions. Additionally, we enhance the model to incorporate the seasonality of specific ecological factors across time. The autonomous and associated nonautonomous models have undergone thorough mathematical analysis and extensive numerical simulations in the course of the study. We conduct a fundamental differential sensitivity analysis to discern the key parameters influencing both prey and predator populations within the ecosystem. Through numerical investigations of the autonomous model, we notice that in the presence (absence) of harvesting, the mutual interference among predators destabilizes (stabilizes) the coexisting equilibrium. The fear effect significantly reduces the densities of prey and predator populations, and destabilizes the coexisting equilibrium by producing multiple stability switches. The survival of predators substantially depends on the focal prey if their growth from other food sources is relatively low. Notably, the harvesting of predators is beneficial and promotes the coexistence of species only when their growth from other food sources is too much. Moreover, the system shows bistability, tristability, and multiple limit cycles under identical ecological conditions. We also show various phenomena that manifest within the seasonally forced model, including the emergence of periodic solutions, higher periodic solutions, bursting patterns, and chaotic dynamics. Remarkably, the influence of seasonal forcing possesses the capability to govern the chaotic dynamics by giving rise to an exceedingly quasi-periodic arrangement in the prey and predator densities.