EFFECTS OF HARVESTING ON THE COEXISTENCE IN PREY-PREDATOR SYSTEMS

Abstract

This thesis examines a prey-predator system subjected to harvesting, with a focus on the influence of effort allocation between prey and predator harvesting. Using a modified deterministic mathematical model, we have established the well-posedness of the model, along with the positivity and boundedness of solutions. By applying the Jacobian matrix and Dulac’s criteria, we have analyzed both the local and global stability of the nonnegative steady states. Furthermore, we have investigated the maximum sustainable yield the system can achieve, as well as the optimal harvesting problem. Several numerical examples are presented to illustrate the key findings of the study.