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

Deviations of Steady States of the Traveling Wave to a Competition Diffusion System with Random Perturbation
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摘要 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. 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.
出处 《Journal of Applied Mathematics and Physics》 2015年第5期496-508,共13页 应用数学与应用物理(英文)
关键词 LOTKA-VOLTERRA COMPETITION Diffusion System Random PERTURBATION TWO-PARAMETER White Noise Lotka-Volterra Competition Diffusion System Random Perturbation Two-Parameter White Noise
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