Stability analysis of a fractional order prey-predator system with nonmonotonic functional response

In this paper, we introduce fractional order of a planar fractional prey-predator system with a nonmonotonic functional response and anti-predator behaviour such that the adult preys can attack vulnerable predators. We analyze the existence and stability of all possible equilibria. Numerical simulations reveal that anti-predator behaviour not only makes the coexistence of the prey and predator populations less likely, but also damps the predator-prey oscillations. Therefore, antipredator behaviour helps the prey population to resist predator aggression.

Keywords:

Bifurcation , Fractional Prey-predator model , Stability of equilibrium , Dynamical behavior , Limit cycle