ANZIAM J.
46 (2004), 121-141
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Persistence and global stability in a delayed predator-prey system with Holling-type functional response
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Rui Xu
Department of Mathematics
Shijiazhuang Mechanical Engineering College
Shijiazhuang 050003
Hebei Province
P.R. China
rxu88@yahoo.com.cn
and
Department of Mathematics
University of Dundee
Dundee DD1 4HN
Scotland
U.K.
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Lansun Chen
Institute of Mathematics
Academia Sinica
Beijing 100080
P.R. China
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M. A. J. Chaplain
Department of Mathematics
University of Dundee
Dundee DD1 4HN
Scotland
U.K.
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Abstract
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A delayed predator-prey system with Holling type
III functional response is investigated. It is
proved that the system is uniformly persistent
under some appropriate conditions. By means of
suitable Lyapunov functionals, sufficient
conditions are derived for the local and global
asymptotic stability of a positive equilibrium of
the system. Numerical simulations are presented
to illustrate the feasibility of our main
results.
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