Persistence and stability for the three species ratio-dependent food–chain model

Abstract

In this paper, we have proposed and analyzed a tritrophic food chain model composed of a prey, a middle predator and a top
predator. Ratio-dependent functional response is considered to model the interactions among the species of the system.
Mathematical analysis of model equation with regard to the nature of equilibria, boundedness and persistence of the solution are
carried out. To verify the analytical findings numerical simulation is performed. Furthermore, global stability of the system is shown graphically. It has been observed from numerical simulation that prey population decreases in the absence of top predators. However, presence of top predators in the system causes an increase in prey population with a depression in the population of middle predators.