ISSN 0869-6632 (Print)
ISSN 2542-1905 (Online)

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Kurushina S. E., Gromova L. I., Maksimov V. V. Stochastic equations and Fokker–Planck equation for the order parameters in the study of the noise-induced spatial patterns dynamics. Izvestiya VUZ. Applied Nonlinear Dynamics, 2011, vol. 19, iss. 5, pp. 45-63. DOI: 10.18500/0869-6632-2011-19-5-45-67

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Language: 
Russian
Heading: 
Applied Problems of Nonlinear Oscillation and Wave Theory
Article type: 
Article
UDC: 
519.2, 517.957
DOI: 
10.18500/0869-6632-2011-19-5-45-67

Stochastic equations and Fokker–Planck equation for the order parameters in the study of the noise-induced spatial patterns dynamics

Autors: 
Kurushina Svetlana Evgenevna, Samara State University
Gromova Lidija Ivanovna, Samara National Research University
Maksimov Valerij Vladimirovich, Samara National Research University
Abstract: 

From the viewpoint of the order parameters concept spatial pattern formation in excitable fluctuating medium was researched analytically. The reaction–diffusion system in external noise was considered as a model of such medium. Stochastic equations for the unstable modes amplitudes (order parameters) and the dispersion equations for the average unstable modes amplitudes were received. Fokker–Planck equation for the order parameters was received. The developed theory allows studying noise–induced effects, including variation boundaries of ordering and disordering phase transitions in dependence on the parameters of external noise.

Key words: 
Spatial patterns
external noise
phase transitions
order parameters
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Received: 
29.07.2011
Accepted: 
29.07.2011
Published: 
30.12.2011
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