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Tuckwell, H.C. (1993) Random Fluctuations at an Equilibrium of a Nonlinear Reaction Diffusion Equation. Applied Mathematics Letters, 6, 79-81.
http://dx.doi.org/10.1016/0893-9659(93)90017-H

has been cited by the following article:

• TITLE: Deviations of Steady States of the Traveling Wave to a Competition Diffusion System with Random Perturbation

  AUTHORS: Xiaorong Hu, Yanbin Tang

  KEYWORDS: Lotka-Volterra Competition Diffusion System, Random Perturbation, Two-Parameter White Noise

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.3 No.5, May 14, 2015

  ABSTRACT: 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.