Mathematical analysis of the influence of prey escaping from prey herd on three species fractional predator-prey interaction model

This research investigates the impact of prey herd dread from the two types of predators using a fractional-order-derivative model. The investigated model considers one type of prey next to predator and super predator. Note that the pray that exhibits herd behavior with the possibility of quitting the group due to the fear generated by the pursuit of predators, it is also considered that there is a predator consumes this prey and a super-predator consumes them both (prey and predator). This dread can be elaborated by the number of the escaped prey from the herd, which influences the evolution of the whole food chain. Our purpose is to study how this fear can affect the existence of the species, where we will discuss it in details through this paper. Indeed, it is obtained that the considered system undergoes an interesting behavior, which is elaborated by the presence of Hopf bifurcation. The obtained mathematical and ecological results are discussed numerically using a numerical scheme used for obtaining the graphical representations.