Global Stability in Nonautonomous Lotka-Volterra Systems of "Pure-Delay-Type"

Author

Xue-Zhong He

Status

Research Report 96-32
Date: August 1996

Abstract

In this paper, nonautonomous Lotka-Volterra systems of "pure-delay-type" are considered and some sufficient conditions on the global asymptotical stability are obtained. As a corollary, we show that, under the conditions of Theorem 2.1 in Kuang (Diff. Integ. Equs., 9 (1996)), the system remains globally asymptotically stable provided the delays are sufficient 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.

Key phrases

Lotka-Volterra nonautonomous system. pure-delay-type. Lyapunov functionals. global asymptotical stability.

AMS Subject Classification (1991)

Primary: 34K15, 34K20, 92A15
Secondary:

Content

The paper is available in the following forms:

TeX dvi format:: 1996-32.dvi.gz (19kB) or 1996-32.dvi (70kB)
PostScript:: 1996-32.ps.gz (64kB) or 1996-32.ps (216kB)

To minimize network load, please choose the smaller gzipped .gz form if and only if your browser client supports it.

Sydney Mathematics and Statistics