Bifurcation Analysis Of The Modified Lotka-Volterra Prey-Predator Model

Abstract

In this study we presented a mathematical model which describes the interaction between prey and predator populations. We considered a modi_ed Lotka-Volterra prey-predator model. The existence and stability of the equilibrium points were studied both analyti- cally and numerically. The existence and positive equilibrium of the system and stability of the equilibrium of the system studied under various conditions. The phase portraits are obtained for di_erent sets of parameter values and initial conditions. Also bifurcation dia- gram are presented for selected range of growth parameter. Finally, numerical simulation has been used to specify the control parameters and con_rm the obtained results.