Author(s)

Xiaorong Hu^1*, Yanbin Tang^2*

¹Department of Mathematics, National University of Defense Technology, Changsha, China.
²School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan, China.

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.

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

Hu, X. and Tang, Y. (2015) Deviations of Steady States of the Traveling Wave to a Competition Diffusion System with Random Perturbation. Journal of Applied Mathematics and Physics, 3, 496-508. doi: 10.4236/jamp.2015.35062.