%0 Journal Article
%T Deviations of Steady States of the Traveling Wave to a Competition Diffusion System with Random Perturbation
%A Xiaorong Hu
%A Yanbin Tang
%J Journal of Applied Mathematics and Physics
%P 496-508
%@ 2327-4379
%D 2015
%I Scientific Research Publishing
%R 10.4236/jamp.2015.35062
%X This paper
considers the asymptotic dynamics of steady states to the Lotka-Volterra
competition diffusion systems with random perturbations by two-parameter white
noise on the whole real line. By the fundamental solution of heat equation, we
get the asymptotic fluctuating behaviors near the stable states respectively.
That is, near the steady state (<i>u</i>,<i>v</i>)=(0,1), the mean value <i>Eu</i>(<i>x</i>,<i>t</i>) is shifted above the equilibrium <i>u</i>=0 and <i>Ev</i>(<i>x</i>,<i>t</i>) is shifted below the equilibrium <i>v</i>=1. However, near the steady state (<i>u</i>,<i>v</i>)=(1,0), the mean
value <i>Eu</i>(<i>x</i>,<i>t</i>) is shifted below the
equilibrium <i>u</i> =1 and <i>Eu</i>(<i>x</i>,<i>t</i>)=0.
%K Lotka-Volterra Competition Diffusion System
%K Random Perturbation
%K Two-Parameter White Noise
%U http://www.scirp.org/journal/PaperInformation.aspx?PaperID=56304