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.