Predator survival analysis of a Prey-Predator system with prey species pool

Abstract In this paper we study prey-predator relationship in the presence of prey species pool. We describe the set of parameters when the predator will survive and find the threshold when you lose predator survival. This is based on analysis of dependence of locally stable equilibrium points on the parameters of the problem especially on the predator natural mortality rate e . In particular we give an interval for e in terms of other parameters where predators survive. This can allow to control the survival of predators by certain actions to move certain parameters to a safe area. We discover also a more complicated dynamics for small mortality rate.