Random perturbations of reaction–diffusion waves in biology
作者： Ezi Wu , Yanbin Tang
DOI: 10.1016/J.WAVEMOTI.2012.04.004
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摘要: Abstract This paper considers the statistical properties of traveling wave fronts scalar FitzHugh–Nagumo equation with random perturbations by two-parameter white noise u t = x + f ( ) e W on whole real line ℛ , where front connects two stable equilibria 0 and 1 reaction function . As well as method Green’s established Tuckwell a bounded domain, we get asymptotic fluctuation behavior states which are boundaries to Nagumo fundamental solution. That is, about lower (upper) state reveal that mean is increased (decreased) zero → ∞
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G.I. Barenblatt, Ia.B. Zeldovich, G.M. Makhviladze, V.B. Librovich, The Mathematical Theory of Combustion and Explosions ,(1985)
G. F. Roach, Green's Functions ,(1982)
Paul C. Fife, Mathematical Aspects of Reacting and Diffusing Systems ,(1979)
Tuckwell Henry C., Spike trains in a stochastic Hodgkin–Huxley system Biosystems. ,vol. 80, pp. 25- 36 ,(2005) , 10.1016/J.BIOSYSTEMS.2004.09.032
Nicholas F Britton, Reaction-diffusion equations and their applications to biology Reaction-diffusion equations and their applications to biology.. ,(1986)
Henry C. Tuckwell, Nonlinear effects in white-noise driven spatial diffusion: General analytical results and probabilities of exceeding threshold Physica A-statistical Mechanics and Its Applications. ,vol. 387, pp. 1455- 1463 ,(2008) , 10.1016/J.PHYSA.2007.10.062
Yanbin Tang, Li Zhou, Stability switch and Hopf bifurcation for a diffusive prey–predator system with delay Journal of Mathematical Analysis and Applications. ,vol. 334, pp. 1290- 1307 ,(2007) , 10.1016/J.JMAA.2007.01.041
P. C. Fife, L. A. Peletier, Nonlinear diffusion in population genetics Archive for Rational Mechanics and Analysis. ,vol. 64, pp. 93- 109 ,(1977) , 10.1007/BF00280092
Henry C. Tuckwell, Statistical properties of perturbative nonlinear random diffusion from stochastic integral representations Physics Letters A. ,vol. 122, pp. 117- 120 ,(1987) , 10.1016/0375-9601(87)90787-0
Yanbin Tang, Jianli Wang, Bifurcation analysis on a reactor model with combination of quadratic and cubic steps Journal of Mathematical Chemistry. ,vol. 46, pp. 1394- 1408 ,(2009) , 10.1007/S10910-009-9523-7