Global asymptotic stability for a diffusion Lotka-Volterra competition system with time delays
Bull. Korean Math. Soc. 2012 Vol. 49, No. 6, 1255-1262
https://doi.org/10.4134/BKMS.2012.49.6.1255
Published online November 30, 2012
Jia-Fang Zhang and Ping-An Zhang
Henan University, Xidian University
Abstract : A type of delayed Lotka-Volterra competition reaction-diffusion system is considered. By constructing a new Lyapunov function, we prove that the unique positive steady-state solution is globally asymptotically stable when interspecies competition is weaker than intraspecies competition. Moreover, we show that the stability property does not depend on the diffusion coefficients and time delays.
Keywords : global asymptotic stability, delays, Lyapunov function
MSC numbers : 35K57, 92D25
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