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

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. Stability and Hopf Bifurcation Analysis of Prey-Predator Mathematical Model with Delay. In this thesis, mathematical model of prey predator with delay was studied. To show Positivity of the solution for the model given. The equilibrium points for the system were calculated. The model under consideration was nonlinear so that it was linearized by Jacobian matrix at the positive equilibrium point. The local stability conditions were proved by using Routh Huwertiz stability criteria and local stability of the model in the absence and presence of delay was studied at the positive equilibrium point by linearizing the model. Finally, Hopf bifurcation condition was well spelled out. Generally the end result is stability by positive equilibrium points.