Analysis of Predator–Prey Model With Inclusion of Temperature Variability in Prey Refugees

One of the central concerns in ecology is assessing the impact of environmental changes, such as global temperature shifts, on the dynamic interactions between predators and prey across diverse ecosystems. This study explores the relationship between prey and predator populations in the context of climate-induced temperature changes. Utilizing linearization and the Lyapunov approach, we analyze the local and global stability of the system’s equilibrium points. Applying Sotomayor’s theorem, we further investigate the local bifurcation of the fixed points. Additionally, the persistence of the model system is studied. The ecological models developed in this research aim to explore the stability of these predator–prey systems and provide insights to prevent the decline of endangered species. Numerical simulations are conducted to study the impact of environmental changes on the proposed models. The simulation results indicate that the temperature dependence of the predator–prey population dynamics is directly proportional to the size of the reserved habitat area for the prey when the temperature is high. These findings suggest that the preservation of sufficient habitat reserves plays a crucial role in promoting the long-term survival of species and stabilizing their ecological interactions.