Time Evolution of the Densities of Three Species Interacting in the Same Ecosystem and the Stability Analysis of Steady States for a Reaction–Diffusion PDE Model

This paper investigates the trends of three different species interacting in the same ecosystem. The study is conducted on the ecosystem which consists of a prey S 1 and two predators S 2 and S 3 in such a way that S 2 is a predator of S 1 and S 3 is a predator of both S 1 and S 2 . In addition, S 1 and S 2 share the same food which is the main food for S 1 and the alternative food for S 2 . A system of three simultaneous nonlinear partial differential equations is used to represent this situation. The local stability of all constant equilibrium points is discussed after showing their feasibility. In addition, a condition for which a coexisting constant equilibrium point is asymptotically globally stable is also investigated. The results showed that the system has eight constant equilibrium points. Five of them are unstable, while the three remaining are asymptotically locally stable under some conditions on the parameters that are involved in the model.