Global stability of mutualistic interactions among three species population model with continuous time delay

This paper deals with the study on a mathematical model consisting of mutualistic interactions among three species with continuous time delay. The delay kernels are being convex combinations of suitable nonnegative and normalized functions, the linear chain trick gives an expanded system of ordinary differential equations with the same stability properties as the original integro-differential system. Global stability is discussed by constructing Lyapunov function. It has been shown that equilibrium state of the model is globally stable. Finally, numerical simulations supporting our theoretical results are also included.