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

A. B. Mundea and M. B. Dhakneb,*

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

Authors :

A. B. Munde^a and M. B. Dhakne^b,*

Author Address :

^a,bDepartment of Mathematics, Dr. Babasaheb Ambedkar Marathwada University, Aurangabad-431 004, India.

*Corresponding author.

Abstract :

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 di.erential equations with the same stability properties as the original integro-di.erential 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.

Keywords :

Mutualism model, local and global stabilities, Lyapunov function, population dynamics, time delay.

DOI :

Article Info :

Received : October 19, 2012; Accepted : February 03, 2013.