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Global stability in delayed nonautonomous Lotka-Volterra type systems without saturated equilibria. (English) Zbl 0843.34077
Systems of delayed nonautonomous Lotka-Volterra type equations are considered. Global asymptotic behavior of such systems is proved by using a new approach. Sufficient conditions are obtained by dropping the requirement of existence of a saturated equilibrium for these systems. Some applications of this method to autonomous Lotka-Volterra type competition systems are shown. Three open problems are proposed in this paper as well.
Reviewer: A.Slavova (Sofia)

34K20 Stability theory of functional-differential equations
34K99 Functional-differential equations (including equations with delayed, advanced or state-dependent argument)