Sensitivity of parameters and the impact of white noise on a generalist predator–prey model with hunting cooperation

In this study, the specific focus is on investigating the influence of environmental fluctuations on a predator–prey system featuring a generalist predator and hunting cooperation. To incorporate environmental fluctuation into the predator–prey model, we introduce perturbations in the birth rate of prey and the death rate of predator density using Gaussian white noise. We conducted a comprehensive analysis of parameter sensitivity within our system and delved into the significance of the initial states of the species. Altering the initial states of the population have been shown to exert a profound influence on both the dynamics of the system and the long-term sustainability of the species. Our study has uncovered the degree of sensitivity exhibited by the system’s parameters and has identified distinct types of sensitivity that manifest under different initial conditions, offering a novel perspective on the dynamics of the system. By simulating the stochastic system, we analyze the fluctuations in the populations within the ecosystem, considering the influence of stochastic perturbations. Our research demonstrates that prey growth rate, carrying capacity, and prey handling time significantly affect the predator species. Initial conditions for both species are vital for ecosystem persistence, especially with low initial prey density leading to predator extinction risk. Additionally, the higher noise levels lead to species extinction, while lower levels support coexistence. Our study on hunting cooperation and environmental fluctuations enhances our understanding of complex ecological systems. The incorporation of stochasticity provides valuable insights into the behavior of the predator and prey populations, highlighting the importance of considering both biological interactions and environmental variability in ecological studies.