Optimal Control Studies for Additional food provided Prey-Predator Systems involving Holling Type III and Type IV Functional Responses
Speaker: Ananth Srinivas, Louisiana State UniversityStudy of ecosystems where the predator is provided with alternate sources of food in addition to the target prey has gained prominence over the years and has become one of the important areas of research for biologists, ecologists, and mathematicians. This is because provision of additional food has proven to be very effective in conserving endangered species as well as controlling invasive or harmful species. Findings from some of the recent studies on additional food provided systems involving Holling type III and type IV responses emphasize the importance of quality and quantity of additional food. They reveal that for an appropriate choice of quality and quantity of additional food, the system can be driven towards a stable coexistence of both species towards the elimination of either of the interacting species. Though these findings are very helpful in the context of biological conservation and bio-control, they could be practically more relevant if the terminal states can be reached in definite time rather than reaching asymptotically. Thus, there is a need to study the controllability aspects of these additional food systems with the goal of achieving the desired outcomes in minimum (finite) time. In this talk, I will be presenting my work on optimal control studies on the type III and type IV additional food systems using two different approaches from control theory: the Maximum Principle approach and the modified Linear Quadratic Regulator approach.