Optimal control of predator-prey models

A review of some models used to model ecological predator-prey populations is summarized. The Lotka-Volterra, Holling Logistic, and Holling-Tanner models are analyzed through linearization with the Jacobian to characterize the equilibrium points, and computer simulations are obtained to observe the trends of the models' trajectories. Additionally, an analysis of papers on optimal control of predator-prey models is presented to show a few different focuses that have already been utilized in the field of optimal control. Finally, an optimal control problem with two bounded controls for the Holling-Tanner predator-prey model is stated and solved. A computer simulation of that control model at selected values of the parameters and several objective functions is also presented. Furthermore, applications of such a control model are discussed in the context of real world predator-prey situations.