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


Xue-Zhong He


Research Report 96-32
Date: August 1996


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


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