Impact of Allee and fear effects in a fractional order prey-predator system incorporating prey refuge.

In this paper, we study the dynamic behaviors of a fractional order predator-prey system, in which the prey population has three effects: Allee effect, fear effect, and shelter effect. First, we prove in detail the positivity, existence, uniqueness, and boundedness of the solutions of the model from the perspective of mathematical analysis. Second, the stability of the system is considered by analyzing the stability of all equilibria and possible bifurcations of the system.

Impact of fear effect and prey refuge on a fractional order prey-predator system with Beddington-DeAngelis functional response.

In this article, a fractional-order prey-predator system with Beddington-DeAngelis functional response incorporating two significant factors, namely, dread of predators and prey shelter are proposed and studied. Because the life cycle of prey species is memory, the fractional calculus equation is considered to study the dynamic behavior of the proposed system. The sufficient conditions to ensure the existence and uniqueness of the system solution are found, and the legitimacy and well posedness in the biological sense of the system solution, such as nonnegativity and boundedness, are proved.