**Periodic solution of a Lotka-Volterra predator-prey model with dispersion and time delays.** / Xu, R.; Chaplain, M. A. J.; Davidson, F. A.

Research output: Contribution to journal › Article

Xu, R, Chaplain, MAJ & Davidson, FA 2004, 'Periodic solution of a Lotka-Volterra predator-prey model with dispersion and time delays' *Applied Mathematics and Computation*, vol 148, no. 2, pp. 537-560. DOI: 10.1016/S0096-3003(02)00918-9

Xu, R., Chaplain, M. A. J., & Davidson, F. A. (2004). Periodic solution of a Lotka-Volterra predator-prey model with dispersion and time delays. *Applied Mathematics and Computation*, *148*(2), 537-560. DOI: 10.1016/S0096-3003(02)00918-9

Xu R, Chaplain MAJ, Davidson FA. Periodic solution of a Lotka-Volterra predator-prey model with dispersion and time delays. Applied Mathematics and Computation. 2004;148(2):537-560. Available from, DOI: 10.1016/S0096-3003(02)00918-9

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title = "Periodic solution of a Lotka-Volterra predator-prey model with dispersion and time delays",

keywords = "Dispersion, Time delay, Periodic solution, Persistence, Global stability",

author = "R. Xu and Chaplain, {M. A. J.} and Davidson, {F. A.}",

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T1 - Periodic solution of a Lotka-Volterra predator-prey model with dispersion and time delays

AU - Xu,R.

AU - Chaplain,M. A. J.

AU - Davidson,F. A.

N1 - dc.publisher: Elsevier

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

M3 - Article

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SP - 537

EP - 560

JO - Applied Mathematics and Computation

T2 - Applied Mathematics and Computation

JF - Applied Mathematics and Computation

SN - 0096-3003

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