Stability and delays in a predator-prey system - II

As a continuation of author's recent work (J. Math. Anal. Appl., 198 (1996) , 355-370), a classical autonomous Lotka-Volterra predator-prey model with variable bounded delays is concerned. By means of Lyapunov functionals, we establish sufficient conditions on the global attractivity of the positive equilibrium of the model. As a corollary, we show that small delays do not change the global stability of the positive equilibrium of the model. An ex plicit estimate of the delays is also derived. We give also an affirmative answer to the open problem proposed in the previous paper. AMS (MOS) subjec t classification: 34D05, 34K20, 92D25.