Mathematical Modeling of the dynamics of Prey-Predator with Scavenger in a closed habitat

Abstract

In this paper we developed a mathematical model which describes the dynamics of prey- predator interaction with scavenger. The model based on Holling type II functional response. Here we tried to develop model using system of non linear differential equation. We solved the equilibrium points and their existence. The positivity and of the solution of the model are also determined. Conditions for local and global stability analysis are studied both analytically and numerically. The study also addresses the effect of extinction of a population and mechanism that three species coexist. As a result the mechanism that three species become coexist if there is large number of prey population compute with small number of predator and average number of scavenger population. The scavenger species also has a great role in stabilizing as well as for coexistence of three species. Numerical simulations are carried out to illustrate the analytical findings. Finally the biological implication of analytical and numerical are discussed critically