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Bull. Korean Math. Soc. 2012; 49(6): 1255-1262
Printed November 30, 2012
https://doi.org/10.4134/BKMS.2012.49.6.1255
Copyright © The Korean Mathematical Society.
Global asymptotic stability for a diffusion Lotka-Volterra competition system with time delays
Jia-Fang Zhang and Ping-An Zhang
Henan University, Xidian University
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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