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Periodic solution and global stability for a nonautonomous competitive Lotka-Volterra diffusion system. (English) Zbl 1197.34084
Summary: A nonautonomous competitive Lotka-Volterra diffusion system is considered. By using the Brouwer fixed point theorem and constructing a suitable Liapunov function, under some appropriate conditions, the system has a unique periodic solution which is globally stable.

34C60Qualitative investigation and simulation of models (ODE)
34C25Periodic solutions of ODE
34D23Global stability of ODE
92D25Population dynamics (general)
Full Text: DOI
[1] Fengying, Wei; Ke, Wang: Global stability and asymptotically periodic solution for nonautonomous cooperative Lotka -- Volterra diffusion system, Appl. math. Comput. 182, 161-165 (2006) · Zbl 1113.92062 · doi:10.1016/j.amc.2006.03.044
[2] Fengying, Wei; Ke, Wang: Almost periodic solution and stability for nonautonomous cooperative Lotka -- Volterra diffusion system, Songliao J. (Natural science edition) 3, 1-4 (2002) · Zbl 1113.92062
[3] Xinzhu, Meng; Lansun, Chen: Periodic solution and almost periodic solution for a nonautonomous Lotka -- Volterra dispersal system with infinite delay, J. math. Anal. appl. 339, 125-145 (2008) · Zbl 1141.34043 · doi:10.1016/j.jmaa.2007.05.084
[4] Yongkun, Li: Positive periodic solutions of periodic neutral Lotka -- Volterra system with state dependent delays, J. math. Anal. appl. 330, 1347-1362 (2007) · Zbl 1118.34059 · doi:10.1016/j.jmaa.2006.08.063
[5] Yuming, Chen; Zhan, Zhou: Stable periodic solution of a discrete periodic Lotka -- Volterra competition system, J. math. Anal. appl. 277, 358-366 (2003) · Zbl 1019.39004 · doi:10.1016/S0022-247X(02)00611-X
[6] Zhengqiu, Zhang; Zhicheng, Wang: Periodic solution for a two-species nonautonomous competition Lotka -- Volterra patch system with time delay, J. math. Anal. appl. 265, 38-48 (2002) · Zbl 1003.34060 · doi:10.1006/jmaa.2001.7682