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Attractors of Hard Turbulence Type in Relaxation Systems

Attractors of Hard Turbulence Type in Relaxation Systems Differential Equations, Vol. 38, No. 12, 2002, pp. 1694–1702. Translated from Differentsial'nye Uravneniya, Vol. 38, No. 12, 2002, pp. 1596–1605. Original Russian Text Copyright c 2002 by Kolesov, Rozov. ORDINARY DIFFERENTIAL EQUATIONS Attractors of Hard Turbulence Type in Relaxation Systems A. Yu.Kolesov and N.Kh. Rozov Yaroslavl State University, Yaroslavl, Russia Moscow State University, Moscow, Russia Received December 14, 2001 Hard turbulence is of interest in connection with the problem of rare catastrophic events in sys- tems that exhibit complex behavior, such as large hurricanes and typhoons in the atmosphere-ocean system, economic crises, various large-scale perturbations in society, revolutions, etc. The research in this eld started with the paper [1] dealing with the well-known Ginzburg{Landau equation w =(1 + ic )w + w (1 + ic )jwj w (1) t 1 2 [here w(t;x) is a complex-valued function and c and c are real parameters]. To be speci c, the 1 2 study revealed that, in the case of two or three spatial variables and large values of c and c , 1 2 this equation exhibits a chaotic mode with rare but extremely large spikes. This phenomenon was termed \hard turbulence." Later, a similar behavior was found [2] in http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Differential Equations Springer Journals

Attractors of Hard Turbulence Type in Relaxation Systems

Kolesovand, A.; Rozov, N.
Differential Equations , Volume 38 (12) – Oct 10, 2004
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References (2)

Publisher
Springer Journals
Copyright
Copyright © 2002 by MAIK "Nauka/Interperiodica"
Subject
Mathematics; Difference and Functional Equations; Ordinary Differential Equations; Partial Differential Equations
ISSN
0012-2661
eISSN
1608-3083
DOI
10.1023/A:1023899811176
Publisher site
See Article on Publisher Site

Abstract

Differential Equations, Vol. 38, No. 12, 2002, pp. 1694–1702. Translated from Differentsial'nye Uravneniya, Vol. 38, No. 12, 2002, pp. 1596–1605. Original Russian Text Copyright c 2002 by Kolesov, Rozov. ORDINARY DIFFERENTIAL EQUATIONS Attractors of Hard Turbulence Type in Relaxation Systems A. Yu.Kolesov and N.Kh. Rozov Yaroslavl State University, Yaroslavl, Russia Moscow State University, Moscow, Russia Received December 14, 2001 Hard turbulence is of interest in connection with the problem of rare catastrophic events in sys- tems that exhibit complex behavior, such as large hurricanes and typhoons in the atmosphere-ocean system, economic crises, various large-scale perturbations in society, revolutions, etc. The research in this eld started with the paper [1] dealing with the well-known Ginzburg{Landau equation w =(1 + ic )w + w (1 + ic )jwj w (1) t 1 2 [here w(t;x) is a complex-valued function and c and c are real parameters]. To be speci c, the 1 2 study revealed that, in the case of two or three spatial variables and large values of c and c , 1 2 this equation exhibits a chaotic mode with rare but extremely large spikes. This phenomenon was termed \hard turbulence." Later, a similar behavior was found [2] in

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Differential Equations – Springer Journals

Published: Oct 10, 2004

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