Title: Dynamics of additional food provided predator-prey system with applications to biological control
Speaker: Prof B S R V Prasad VIT University, Vellore
Date: 20 September 2012
Time: 4:00 p.m.- 5:00 p.m.
Venue: Department of Mathematics, LH-III
Necessity to understand the role of additional food as a tool in biological control programs is being increasingly felt, particularly due to its Eco-friendly nature. In this present talk, we develop/analyse a variation of standard predator-prey model with Holling type II function response which presents predator-prey dynamics in presence of some additional food to predators. The aim is to study the consequences of providing additional food on the system dynamics. A thorough mathematical analysis reveals that handling times for the available foods play a vital role in determining the eventual state of the system. It is interesting to observe that by varying the quality (characterised by the handling times) and quantity of additional food we can not only control and limit the prey, but also limit and eradicate the predators. In the context of biological pest control, the results caution the manager on the choice of quality and quantity of the additional food used for this purpose. We further study the controllability aspects of the predator-prey system by considering quality of the additional food as the control variable. Control strategies are offered to steer the system from a given initial state to a required terminal state in a minimum time by formulating Mayer problem of optimal control. It is observed that an optimal strategy is a combination of bang-bang controls and could involve multiple switches. Properties of optimal paths are derived using necessary conditions for Mayer problem. In the light of the results evolved in this work it is possible to eradicate the prey from the system in the minimum time by providing the predator with high quality additional food, which is relevant in the pest management. In the perspective of biological conservation this study highlights the possibilities to drive the state to an admissible interior equilibrium (irrespective of its stability nature) of the system in a minimum time.