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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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519.2, 517.957

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

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

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.

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