Periodic solution of a Lotka-Volterra predator-prey model with dispersion and time delays. / Xu, R.; Chaplain, M. A. J.; Davidson, F. A.
In: Applied Mathematics and Computation, Vol. 148, No. 2, 2004, p. 537-560.Research output: Contribution to journal › Article
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TY - JOUR
T1 - Periodic solution of a Lotka-Volterra predator-prey model with dispersion and time delays
A1 - Xu,R.
A1 - Chaplain,M. A. J.
A1 - Davidson,F. A.
AU - Xu,R.
AU - Chaplain,M. A. J.
AU - Davidson,F. A.
PY - 2004
Y1 - 2004
N2 - A periodic Lotka–Volterra predator–prey model with dispersion and time delays is investigated. By using Gaines and Mawhin’s continuation theorem of coincidence degree theory and by means of a suitable Lyapunov functional, a set of easily verifiable sufficient conditions are derived for the existence, uniqueness and global stability of positive periodic solutions of the system. Sufficient conditions are also established for the uniform persistence of the system. Numerical simulations are presented to illustrate our main results.
AB - A periodic Lotka–Volterra predator–prey model with dispersion and time delays is investigated. By using Gaines and Mawhin’s continuation theorem of coincidence degree theory and by means of a suitable Lyapunov functional, a set of easily verifiable sufficient conditions are derived for the existence, uniqueness and global stability of positive periodic solutions of the system. Sufficient conditions are also established for the uniform persistence of the system. Numerical simulations are presented to illustrate our main results.
KW - Dispersion
KW - Time delay
KW - Periodic solution
KW - Persistence
KW - Global stability
U2 - 10.1016/S0096-3003(02)00918-9
DO - 10.1016/S0096-3003(02)00918-9
M1 - Article
JO - Applied Mathematics and Computation
JF - Applied Mathematics and Computation
SN - 0096-3003
IS - 2
VL - 148
SP - 537
EP - 560
ER -