NONLINEAR MULTIVARIATE SELFCONSISTENT FOKKER–PLANCK EQUATION FOR MULTICOMPONENT REACTIONDIFFUSION SYSTEMS
Cite this article as:
Kurushina S. Е., Gromova L. ., Shapovalova Е. А. NONLINEAR MULTIVARIATE SELFCONSISTENT FOKKER–PLANCK EQUATION FOR MULTICOMPONENT REACTIONDIFFUSION SYSTEMS. Izvestiya VUZ. Applied Nonlinear Dynamics, 2014, vol. 22, iss. 5, pp. 27-42. DOI: https://doi.org/10.18500/0869-6632-2014-22-5-27-42
Mean field approximation is extended to multicomponent stochastic reactiondiffusion systems. A multivariate nonlinear selfconsistent Fokker–Planck equation defining the probability density of the state of the system, which describes a wellknown model of autocatalytic chemical reaction (Brusselator) with spatially correlated multiplicative noise, is obtained. The evolution of probability density and statistical characteristics of the system in the region of Turing bifurcation are studied. Numerical study of the equation solutions for a stochastic brusselator shows that in the region of Turing bifurcation several types of solutions exist if noise intensity increases: unimodal solution, transient bimodality, and an interesting solution which involves multiple «repumping» of probability density through bimodality.
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BibTeX
author = {S. Е. Kurushina and L. I. Gromova and Еu. А. Shapovalova},
title = {NONLINEAR MULTIVARIATE SELFCONSISTENT FOKKER–PLANCK EQUATION FOR MULTICOMPONENT REACTIONDIFFUSION SYSTEMS},
year = {2014},
journal = {Izvestiya VUZ. Applied Nonlinear Dynamics},
volume = {22},number = {5},
url = {https://old-andjournal.sgu.ru/en/articles/nonlinear-multivariate-selfconsistent-fokker-planck-equation-for-multicomponent},
address = {Саратов},
language = {russian},
doi = {10.18500/0869-6632-2014-22-5-27-42},pages = {27--42},issn = {0869-6632},
keywords = {Mean field approximation,reactiondiffusion systems,nonlinear selfconsistent Fokker–Planck equation,numerical solution of Fokker–Planck equation.},
abstract = {Mean field approximation is extended to multicomponent stochastic reactiondiffusion systems. A multivariate nonlinear selfconsistent Fokker–Planck equation defining the probability density of the state of the system, which describes a wellknown model of autocatalytic chemical reaction (Brusselator) with spatially correlated multiplicative noise, is obtained. The evolution of probability density and statistical characteristics of the system in the region of Turing bifurcation are studied. Numerical study of the equation solutions for a stochastic brusselator shows that in the region of Turing bifurcation several types of solutions exist if noise intensity increases: unimodal solution, transient bimodality, and an interesting solution which involves multiple «repumping» of probability density through bimodality. }}