The Optimal Harvesting Strategy of A Discretized Stage-Structured Prey-Predator Fractional Model with Crowley-Martin Functional Response

Abstract

     This paper focuses on studying the dynamical behavior of a discrete-time stage structured prey-predator fractional model with Crowley-Martin type functional response. This study starts with the construction of a discretization of the fractional stage structured prey-predator model by using piecewise constant arguments process then we determine and set conditions that are required to achieve the local stability of all the equilibrium points of the considered system. The results of the study show that the discrete–fractional system may have one or two non-negative interior equilibrium points. One of them becomes locally asymptotically stable under certain conditions. Also, we present and extend the considered system to the optimal control problem to get maximum harvest profit strategy. For that, the Pontryagin’s maximal principal to get the optimal solution is applied. Numerical simulation is given to verify the analytical results.