A Theoretical Study on the dynamical behavior of a fractional order predator-prey model with Crowley-Martin function in presence of memory effects

Source abstract

In this paper, the dynamical behavior of an improved stage-structured fractional-order predator-prey model with Crowley-Martin function is discussed theoretically. Following fractional order Caputo derivative approach, here I first convert the integer order stage-structured prey-predator model into the fractional order model. Qualitative behaviors like existence, uniqueness and non-negativity which are thoroughly discussed in a feasible region for fractional order system. Local stability criteria of the different equilibrium points have been discussed for fractional order system. Global stability of the interior equilibrium point have been proved rigorously by defining suitable Lyapunov function. Theoretically, it has been observed that the fractional order system shows more complex dynamics for lower memory as the fractional order becomes larger and shows more simpler dynamics for higher memory as the order $m$ decreases. Specially, due to memory effect, it becomes stable for lower value of $m$ and the dynamics of the fractional-order system not only depends on system parameters but also depends on fractional order $m$.