Dynamics and Control of a Predator-Prey System with the Supply of Additional Food to Predators

Abstract

This thesis examines the efficient and important role of additional food in a predator-prey system. In this work, we derive and study a model for two species. The prey population is assumed to be growing logistically in absence of predators, with the predators having an additional food (nonprey) source apart from natural prey and the functional response is assumed to be ratio-dependent. This leads to the development of a modified ratio-dependent model. We study the modified ratio dependent model via stability (local and global) analysis and analyze the consequences of providing additional food to the predators. By taking the spatial component into account we consider a diffusive modified ratio-dependent model and obtain the necessary conditions for Turing instability to occur. We determine the role of additional food supply in the formation of Turing patterns. We also look into the effect of prey harvesting in the system with and without additional food supply to predators. This is accomplished by examining the stability analysis results and obtaining the optimal harvesting policy for both the ratio-dependent and modified ratio-dependent model with prey harvesting. Finally, we study a minimum time optimal control problem for controlling pest (prey) population, where the quality of additional food is taken as the control variable.