Impact of Hunting Cooperation and Fear Effect on a Tritrophic Food Chain Model

Considering the importance of food chains in the environment from both biological and economic points of view, the life of a living organism depends on the existence of organisms that precede it. Many predators have also developed their own methods of obtaining food, although there is competition among them. Thus, studying hunting cooperation, which is typical of some predators, and the resulting fear of prey and its impact on food chain dynamics, is essential to understanding and controlling the presence and stability of those food chains. Therefore, the influence of hunting cooperation and the fear effect in a three-species food chain model was investigated in this paper. The feeding process was represented by a Holling Type II functional response at each level of the chain. Intraspecific competition among predator species was also taken into account. The system solution’s features are investigated. The analysis of the system’s equilibria’s local and global stability was explored. The food chain model’s persistence conditions were determined. The necessary conditions for the occurrence of local bifurcation around the equilibria were established. To determine the presence of chaos in the food chain system, bifurcation diagrams were obtained. It is discovered that the system has rich dynamics, including point attractors, periodic attractors, and strange attractors.