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