By means of Lyapunov functional, we have succeeded in establishing the global asymptotic stability of the positive solutions of a delayed n-species nonautonomous Lotka-Volterra type competitive system without dominating instantaneous negative feedbacks. As a corollary, we show that the global asymptotic stability of the positive solution is maintained provided that the delayed negative feedbacks dominate other interspecific interaction effects with delays and the mean delays are sufficiently small.
- Lyapunov functional
- Global asymptotic stability
- Infinite delay
- Nonautonomous Lotka-Volterra competitive system
Xu, R., Chaplain, M. A. J., & Chen, L. (2002). Global asymptotic stability in n-species nonautonomous Lotka-Volterra competitive systems with infinite delays. Applied Mathematics and Computation, 130(2), 295-309. https://doi.org/10.1016/S0096-3003(01)00097-2