TIME OPTIMAL CONTROL STUDIES AND SENSITIVITY ANALYSIS OF ADDITIONAL FOOD PROVIDED PREY–PREDATOR SYSTEMS INVOLVING HOLLING TYPE III FUNCTIONAL RESPONSE BASED ON QUALITY OF ADDITIONAL FOOD

Abstract

Research on additional food provided prey–predator systems has gained prominence over the years due to its relevance in the context of biological conservation and pest management. Studies in this area suggest that the system can be driven to any desired state asymptotically with appropriate quality and quantity of additional food. In this paper, we study the controllability aspects to drive the system to the desired state in minimum (finite) time to make the outcomes practically more viable. We consider an additional food provided prey–predator system involving Holling type III functional response and study its controllability based on the quality of additional food, keeping the quantity fixed. To that end, we first analyze the dynamics of the system based on quality. Then, we formulate and study a time optimal control problem with the quality of additional food as the control parameter by proving the existence of optimal control and studying its characteristics. Finally, we illustrate the theoretical findings of the work using numerical simulations.