Xu, Rui; Chen, Lansun; Chaplain, M. A. J. Gobal asymptotic stability in \(n\)-species nonautonomous Lotka-Volterra competitive systems with delays. (English) Zbl 1033.34078 Acta Math. Sci., Ser. B, Engl. Ed. 23, No. 2, 208-218 (2003). Summary: A delayed \(n\)-species nonautonomous Lotka-Volterra-type competitive system without dominating instantaneous negative feedback is investigated. By means of a suitable Lyapunov functional, sufficient conditions are derived for the global asymptotic stability of the positive solutions to the system. As a corollary, it is shown 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 delays are sufficiently small. Cited in 3 Documents MSC: 34K20 Stability theory of functional-differential equations 92D25 Population dynamics (general) Keywords:global asymptotic stability; \(n\)-species nonautonomous Lotka-Volterra competitive systems; Lyapunov functional; delayed negative feedbacks PDFBibTeX XMLCite \textit{R. Xu} et al., Acta Math. Sci., Ser. B, Engl. Ed. 23, No. 2, 208--218 (2003; Zbl 1033.34078) Full Text: DOI