GLOBAL ASYMPTOTIC STABILITY IN N-SPECIES NONAUTONOMOUS LOTKA-VOLTERRACOMPETITIVE SYSTEMS WITH DELAYS

Abstract

Abstract:

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 of 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.

Key words: Nonautonomous Lotka-Volterra competitive system, finite and infinite delay,global asymptotic stability, Lyapunov functional

CLC Number:

34D23

XU Rui, CHEN Lan-Sun,M.A.J. Chaplain. GLOBAL ASYMPTOTIC STABILITY IN N-SPECIES NONAUTONOMOUS LOTKA-VOLTERRACOMPETITIVE SYSTEMS WITH DELAYS[J].Acta mathematica scientia,Series B, 2003, 23(2): 208-.

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