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This article is cited in 1 scientific paper (total in 1 paper)
Statistical structuring theory in parametrically excitable dynamical systems with a Gaussian pump
V. I. Klyatskina, K. V. Koshel'bc a Obukhov Institute of Atmospheric Physics, RAS, Moscow,
Russia
b Il'ichev Pacific Oceanological Institute, Far Eastern
Division, RAS, Vladivostok, Russia
c Far Eastern Federal University, Vladivostok, Russia
Abstract:
Based on the idea of the statistical topography, we analyze the problem of emergence of stochastic structure formation in linear and quasilinear problems described by first-order partial differential equations. The appearance of a parametric excitation on the background of a Gaussian pump is a specific feature of these problems. We obtain equations for the probability density of the solutions of these equations, whence it follows that the stochastic structure formation emerges with probability one, i.e., for almost every realization of the random parameters of the medium.
Keywords:
Liouville equation, diffusion approximation, probability density, integral probability distribution function, typical realization curve, statistical topography, clustering.
Received: 02.03.2015 Revised: 20.05.2015
Citation:
V. I. Klyatskin, K. V. Koshel', “Statistical structuring theory in parametrically excitable dynamical systems with a Gaussian pump”, TMF, 186:3 (2016), 475–495; Theoret. and Math. Phys., 186:3 (2016), 411–429
Linking options:
https://www.mathnet.ru/eng/tmf8882https://doi.org/10.4213/tmf8882 https://www.mathnet.ru/eng/tmf/v186/i3/p475
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