Persistence and global stability of a ratio-dependent predator-prey model with stage structure. / Xu, Rui; Chaplain, M. A. J.; Davidson, F. A.
In: Applied Mathematics and Computation, Vol. 158, No. 3, 11.2004, p. 729-744.Research output: Contribution to journal › Article
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TY - JOUR
T1 - Persistence and global stability of a ratio-dependent predator-prey model with stage structure
A1 - Xu,Rui
A1 - Chaplain,M. A. J.
A1 - Davidson,F. A.
AU - Xu,Rui
AU - Chaplain,M. A. J.
AU - Davidson,F. A.
PY - 2004/11
Y1 - 2004/11
N2 - A ratio-dependent predator–prey model with stage structure for prey is investigated. First, sufficient conditions are derived for the uniform persistence and impermanence of the model. Next, by constructing appropriate Lyapunov functions, a set of easily verifiable sufficient conditions are obtained for the global asymptotic stability of nonnegative equilibria of the model. Numerical simulations are presented to illustrate the validity of our main results.
AB - A ratio-dependent predator–prey model with stage structure for prey is investigated. First, sufficient conditions are derived for the uniform persistence and impermanence of the model. Next, by constructing appropriate Lyapunov functions, a set of easily verifiable sufficient conditions are obtained for the global asymptotic stability of nonnegative equilibria of the model. Numerical simulations are presented to illustrate the validity of our main results.
KW - Ratio-dependence
KW - Predator-prey model
KW - Stage structure
KW - Uniform persistence
KW - Global stability
U2 - 10.1016/j.amc.2003.10.012
DO - 10.1016/j.amc.2003.10.012
M1 - Article
JO - Applied Mathematics and Computation
JF - Applied Mathematics and Computation
SN - 0096-3003
IS - 3
VL - 158
SP - 729
EP - 744
ER -