Differential and Integral Equations

Global stability in nonautonomous Lotka-Volterra systems of "pure-delay type"

Xue-Zhong He

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Abstract

In this paper, nonautonomous Lotka--Volterra systems of "pure-delay type" are considered and some sufficient conditions on the global asymptotic stability are obtained. As a corollary, we show that, under the conditions of Theorem 2.1 in Kuang [11], the system remains globally asymptotically stable provided the delays are sufficiently small. Both finite and infinite delays are allowed in the systems. Our results give an affirmative answer to the two open problems due to Kuang. The results are established by constructing suitable Lyapunov functionals.

Article information

Source
Differential Integral Equations, Volume 11, Number 2 (1998), 293-310.

Dates
First available in Project Euclid: 30 April 2013

Permanent link to this document
https://projecteuclid.org/euclid.die/1367341072

Mathematical Reviews number (MathSciNet)
MR1741847

Zentralblatt MATH identifier
1022.34068

Subjects
Primary: 34K20: Stability theory
Secondary: 34K60: Qualitative investigation and simulation of models 92D25: Population dynamics (general)

Citation

He, Xue-Zhong. Global stability in nonautonomous Lotka-Volterra systems of "pure-delay type". Differential Integral Equations 11 (1998), no. 2, 293--310. https://projecteuclid.org/euclid.die/1367341072


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