The Dynamics and Optimal Control of a Prey Predator System
In this paper, we consider a two dimensional continuous preypredator of first order differential equations. All the possible its equilibria and their local stability are investigated. This autonomous system is then extended to an optimal control model by proposing a control variable, which reduces the risk of extinction of the prey population. Thus the goal of this control is to reduce the number of the predator density. For this aim the Pontryagin's maximum principle has been applied. We also establish the necessary conditions and the characterization for the optimal solutions. Finally, some numerical simulations are presented to support the theoretical conclusions.