Some general problems concerning the stochastic approach are discussed in relation to parametrically excited stochastic dynamic systems described by partial differential equations. Such problems arise in hydrodynamics, magnetohydrodynamics, and astro, plasma, and radio physics and share the feature that the statistical characteristics of their solutions (moments, correlation and spectral functions, and so on) increasing exponentially with time, whereas some solution implementations lead to the formation of random structures with probability one as a result of clustering. The goal of this paper is to use the ideas of stochastic topography to find conditions under which such structures arise.

PACS: 05.40.−a, 05.45.−a, 46.65.+g, 47.27.−i (all) DOI: 10.3367/UFNe.0181.201105a.0457 URL: https://ufn.ru/en/articles/2011/5/a/ 000294814900001 2-s2.0-80051865900 2011PhyU...54..441K Citation: Klyatskin V I "Integral characteristics: a key to understanding structure formation in stochastic dynamic systems" Phys. Usp. 54 441–464 (2011) BibTexBibNote ® (generic)BibNote ® (RIS)MedlineRefWorks Received: 12th, August 2010, revised: 1st, November 2010, accepted: 16th, November 2010 Оригинал: Кляцкин В И «Интегральные характеристики — ключ к пониманию структурообразования в стохастических динамических системах» УФН 181 457–482 (2011); DOI: 10.3367/UFNr.0181.201105a.0457