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 (u,v)=(0,1), the mean value Eu(x,t) is shifted above the equilibrium u=0 and Ev(x,t) is shifted below the equilibrium v=1. However, near the steady state (u,v)=(1,0), the mean
value Eu(x,t) is shifted below the
equilibrium u =1 and Eu(x,t)=0.
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