Bifurcation analysis and fear-induced reactions in non-refuged prey with cooperative hunting among predators:...

The impacts of fear, refuge-seeking behavior of prey, and modified cooperative hunting among predators are collectively included in a mathematical model to explore predator-prey dynamics. The stability of the system's equilibrium points and the occurrence of different bifurcations are analyzed. The system exhibits bistability, characterized by the presence of two stable equilibrium points. Numerical investigation reveals that elevated fear levels simplify the species' coexistence, even when considering increased refuge and prey birth rate. When hunting cooperation rate is extremely high, prey survival becomes unsustainable, particularly with lower birth rate, unless refuge is sought. Conversely, ample refuge capacity allows prey to persist despite lower birth rates. To create time-series solutions and examine stationary distributions, we run multiple simulations. Notably, species have a tendency to fluctuate around the mean values of the deterministic state when there are minimal external disruptions. Interestingly, an increased noise intensity on predators shifts the system's dynamics to a predator-free equilibrium from coexistence of prey and predators.