An Optimal Control Problem for a Predator-Prey Reaction-Diffusion System
Mathematical Modelling of Natural Phenomena, 2010, 5(6): 180-195.
An optimal control problem is studied for a predator-prey system of PDE, with a logistic growth rate of the prey and a general functional response of the predator. The control function has two components. The purpose is to maximize a mean density of the two species in their habitat. The existence of the optimal solution is analyzed and some necessary optimality conditions are established. The form of the optimal control is found in some particular cases.
adjoint system; functional response of the predator; logistic growth rate; maximum principle; optimality conditions