Effects of predator cooperation in hunting and prey fear in a generalist predator-prey model that includes global warming phenomena

Emissions of greenhouse gases from human activities are the cause of global warming. Some of the repercussions include habitat loss, altered competitive relationships, and temperature and ecosystem changes that are too large for migration. According to this study, the carrying capacity is affected by global warming. Furthermore, by developing a predation function that accounts for the effects of hunting cooperation and global warming, its influence on predation has been examined. The interaction between prey, predators, and global warming is described by a system of ordinary differential equations that includes the components listed above. During our investigation, we examine the existence and stability of equilibrium points, which reveals the model's dynamic behaviors. Our model shows a range of bifurcations, including Hopf, transcritical, and saddle-node bifurcations, which mark critical shifts in system dynamics. To confirm these bifurcations, we derive and verify transversality conditions. Additionally, we construct one- and two-parameter bifurcation diagrams to visualize stability changes across the parameter space, identifying regions with distinct steady states and dynamic behaviors. Notably, our model also exhibits switching behavior, where shifts in parameters lead to transitions between different dynamic states, highlighting the complexity and richness of prey-predator interactions.