Global stability of a Lotka-Volterra type predator-prey model with stage structure and time delay. / Xu, Rui; Chaplain, M. A. J.; Davidson, F. A.
In: Applied Mathematics and Computation, Vol. 159, No. 3, 2004, p. 863-880.Research output: Contribution to journal › Article
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TY - JOUR
T1 - Global stability of a Lotka-Volterra type predator-prey model with stage structure and time delay
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
Y1 - 2004
N2 - A delayed Lotka-Volterra type predator-prey model with stage structure for predator is investigated. It is assumed in the model that the individuals in the predator population may belong to one of two classes: the immatures and the matures, the age to maturity is presented by a time delay, and that the immature predators do not have the ability to prey. By analyzing characteristic equations and using an iterative technique, a set of easily verifiable sufficient conditions are derived for the local and global stability of the nonnegative equilibria of the model. Numerical simulations are carried out to illustrate the validity of our results.
AB - A delayed Lotka-Volterra type predator-prey model with stage structure for predator is investigated. It is assumed in the model that the individuals in the predator population may belong to one of two classes: the immatures and the matures, the age to maturity is presented by a time delay, and that the immature predators do not have the ability to prey. By analyzing characteristic equations and using an iterative technique, a set of easily verifiable sufficient conditions are derived for the local and global stability of the nonnegative equilibria of the model. Numerical simulations are carried out to illustrate the validity of our results.
KW - Stage structure
KW - Time delay
KW - Characteristic equation
KW - Global stability
U2 - 10.1016/j.amc.2003.11.008
DO - 10.1016/j.amc.2003.11.008
M1 - Article
JO - Applied Mathematics and Computation
JF - Applied Mathematics and Computation
SN - 0096-3003
IS - 3
VL - 159
SP - 863
EP - 880
ER -