Stability and Bifurcation Analysis of Prey-Predator Mathematical Model with Delay and Control of the Predator

Abstract

The dynamic relationship between predators and their prey has long been and will continue to be one of the dominant themes of research in applied mathematics and ecology. In this thesis, mathematical model of prey predator with delay was studied. Firstly, local stability of the model in the absence and presence of delay was studied at the positive equilibrium point by l inearizing the model. Secondly, the existence of global stability was proved by the aid of Lyapunov theorem. Thirdly, non-existence of limit cycle at positive equilibrium was checked by Dulac’s criterion and the limit cycle exists if there is no intraspecific competition rate of prey. Finally, Hopf bifurcation condition was well spelled out.