Stability and Bifurcation in a Prey–Predator–Scavenger System with Michaelis–Menten Type of Harvesting Function

In this paper an ecological model consisting of prey–predator–scavenger involving Michaelis–Menten type of harvesting function is proposed and studied. The existence, uniqueness and uniformly bounded of the solution of the proposed model are discussed. The stability and persistence conditions of the model are established. Lyapunov functions are used to study the global stability of all equilibrium points. The possibility of occurrence of local bifurcation around the equilibrium points is investigated. Finally an extensive numerical simulation is carried out to validate the obtained analytical results and understand the effects of scavenger and harvesting on the model dynamics. It is observed that the proposed model is very sensitive for varying in their parameters values especially those related with scavenger and undergoes different types of local bifurcation.