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Volume 9,     Number 1,     Spring 2001

 

STABILITY ANALYSIS OF A VOLTERRA PREDATOR-PREY SYSTEM WITH TWO DELAYS
YANBIN TANG, EDOARDO BERETTA AND FORTUNATA SOLIMANO

Abstract. The objective of this paper is to systematically study the qualitative properties of a predator-prey system with two delays. First, we investigate the effect of two distinct delays on stability of the unique positive equilibrium by analyzing the corresponding characteristic equation. The stability criteria involving the delays and the parameters are given. Second, we prove a permanence result for the system. Third, we describe the global stability of the positive equilibrium while the sum of two delays is small, via constructing a proper Liapunov functional in a restricted region. Finally, we give an example to show the application of our results.

 

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