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Global stability in nonautonomous Lotka-Volterra systems of “pure-delay type”. (English) Zbl 1022.34068
From the author’s abstract: Here, nonautonomous Lotka-Volterra systems of “pure-delay-type” [cf. V. B. Kolmanovskij, L. Torelli and R. Vermiglio, SIAM J. Math. Anal. 25, 948-961 (1994; Zbl 0808.34086)] are considered and some sufficient conditions for the global asymptotic stability are obtained. As a corollary, it is shown that, under the conditions of theorem 2.1 from Y. Kuang [Differ. Integral Equ. 9, 557-567 (1996; Zbl 0843.34077)], the system remains globally asymptotically stable provided the delays are sufficiently small. Both finite and infinite delays are allowed in the systems. The results of the author are established by constructing suitable Lyapunov functionals and give an affirmative answer to the two open problems due to Kuang.

34K20 Stability theory of functional-differential equations
92D25 Population dynamics (general)