Global Stability in Nonautonomous Lotka-Volterra Systems of "Pure-Delay-Type"
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.
Lotka-Volterra nonautonomous system. pure-delay-type.
Lyapunov functionals. global asymptotical stability.
AMS Subject Classification (1991)
Primary: 34K15, 34K20, 92A15
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Sydney Mathematics and Statistics