Author:
A. B. Munde ,M. B. Dhakne
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 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.
Subject
Geology,Ocean Engineering,Water Science and Technology
Reference14 articles.
1. E. Beretta and Y. Takeuchi, Global stability of single species diffusion Volterra models continuous time delays, Bulletin of Mathematical Biology, 49(4)(1987), 431-448.
2. A.W. Busekros, Global stability in ecological systems with continuous time delay, SIAM J. Appl. Math., 35(1)(1978), 123-134.
3. J.M. Cushing, Integro-differential equations and delay models in population dynamics, Lecture-Notes in Biomathematics, No. 20, Springer-Verlag, Berlin, 1977.
4. C.H. Feng and P.H. Chao, Global stability for the Lotka Volterra mutualistic system with time delay, Tunghai Science, 8(2006), 81-107.
5. K. Gopalsamy, Stability on the oscillations in delay differential equations of population dynamics, Academic Press, New York, 1993.