An Optimal Control Policy for A Discrete Model with Holling-Tanner Functional Response

Sadiq Al-Nassir


A two dimensional discrete time prey-predator model with Holling-Tanner functional response is considered. The local behavior of all its equilibria are investigated. An optimal control problem with this model is proposed, which aims to increase the number of the prey density to prevent the risk of extinction. The Pontryagin’s maximum principle for discrete system is applied to achieve the optimality. The necessary conditions and the characterization for the optimal solutions of this system is derived. Finally, we present some numerical simulations to support the theoretical conclusions.


Holling-Tanner functional response; Local stability; Discrete optimal control

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