TY  - JOUR
T1  - Global stability of a stage-structured predator-prey model with prey dispersal
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  - 2005
Y1  - 2005
N2  - A delayed Lotka–Volterra type predator-prey model with stage structure for predator and prey dispersal in two-patch environments is investigated. It is assumed that immature individuals and mature individuals of predator species are divided by a fixed age, and that immature predators do not feed on prey and do not have the ability to reproduce; on the other hand, it is assumed that the prey species can disperse between one patch with a low level of food and without predation and one patch with a higher level of food but with predation. By means of two different kinds of Lyapunov functionals, sufficient conditions are derived respectively for the global asymptotic stability of a positive equilibrium of the model. By analyzing the characteristic equation, criterion is established for the local stability of the positive equilibrium. Numerical simulations are presented to illustrate our main results.
AB  - A delayed Lotka–Volterra type predator-prey model with stage structure for predator and prey dispersal in two-patch environments is investigated. It is assumed that immature individuals and mature individuals of predator species are divided by a fixed age, and that immature predators do not feed on prey and do not have the ability to reproduce; on the other hand, it is assumed that the prey species can disperse between one patch with a low level of food and without predation and one patch with a higher level of food but with predation. By means of two different kinds of Lyapunov functionals, sufficient conditions are derived respectively for the global asymptotic stability of a positive equilibrium of the model. By analyzing the characteristic equation, criterion is established for the local stability of the positive equilibrium. Numerical simulations are presented to illustrate our main results.
KW  - Stage structure
KW  - Time delay
KW  - Dispersal
KW  - Permanence
KW  - Global stability
U2  - 10.1016/j.amc.2005.01.055
DO  - 10.1016/j.amc.2005.01.055
M1  - Article
JO  - Applied Mathematics and Computation
JF  - Applied Mathematics and Computation
SN  - 0096-3003
IS  - 1
VL  - 171
SP  - 293
EP  - 314
ER  -