MR2997965 (Review) 37D45Viana, R. L.; Lopes, S. R.;Szezech, J.D., Jr.; Caldas, I. L.Synchronization of chaos and the transition to wave turbulence.Internat. J. Bifur. Chaos Appl. Sci. Engrg. 22 (2012), no. 10, 1250234, 9 pp.1793-6551

Risultato della ricerca: Review article

Abstract

In this paper the authors analyze the onset of the wave turbulence in the spatially extended threewaveinteracting model by using the concept of synchronization. In order to work with a setof ordinary differential equations, they make a pseudo-spectral decomposition of the wave fieldand identify the onset of wave turbulence as the excitation of spatial modes in the presence ofunderlying temporally chaotic dynamics. Each spatial point is regarded as a nonlinear oscillatorand the onset of wave turbulence is the point where the oscillators lose phase synchronization.The authors use an extremely sensitive complex-order parameter to estimate the threshold of weakturbulence and perform a Lyapunov analysis leading to the detection of the so-called blowoutbifurcation.
Lingua originaleEnglish
Numero di pagine0
RivistaMATHEMATICAL REVIEWS
Volume2013
Stato di pubblicazionePublished - 2013

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chaos
synchronism
turbulence
differential equations
oscillators
decomposition
thresholds
estimates
excitation

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title = "MR2997965 (Review) 37D45Viana, R. L.; Lopes, S. R.;Szezech, J.D., Jr.; Caldas, I. L.Synchronization of chaos and the transition to wave turbulence.Internat. J. Bifur. Chaos Appl. Sci. Engrg. 22 (2012), no. 10, 1250234, 9 pp.1793-6551",
abstract = "In this paper the authors analyze the onset of the wave turbulence in the spatially extended threewaveinteracting model by using the concept of synchronization. In order to work with a setof ordinary differential equations, they make a pseudo-spectral decomposition of the wave fieldand identify the onset of wave turbulence as the excitation of spatial modes in the presence ofunderlying temporally chaotic dynamics. Each spatial point is regarded as a nonlinear oscillatorand the onset of wave turbulence is the point where the oscillators lose phase synchronization.The authors use an extremely sensitive complex-order parameter to estimate the threshold of weakturbulence and perform a Lyapunov analysis leading to the detection of the so-called blowoutbifurcation.",
keywords = "Synchronization of chaos, onset of turbulence, wave turbulence",
author = "Gaetana Gambino",
year = "2013",
language = "English",
volume = "2013",
journal = "MATHEMATICAL REVIEWS",
issn = "0025-5629",

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TY - JOUR

T1 - MR2997965 (Review) 37D45Viana, R. L.; Lopes, S. R.;Szezech, J.D., Jr.; Caldas, I. L.Synchronization of chaos and the transition to wave turbulence.Internat. J. Bifur. Chaos Appl. Sci. Engrg. 22 (2012), no. 10, 1250234, 9 pp.1793-6551

AU - Gambino, Gaetana

PY - 2013

Y1 - 2013

N2 - In this paper the authors analyze the onset of the wave turbulence in the spatially extended threewaveinteracting model by using the concept of synchronization. In order to work with a setof ordinary differential equations, they make a pseudo-spectral decomposition of the wave fieldand identify the onset of wave turbulence as the excitation of spatial modes in the presence ofunderlying temporally chaotic dynamics. Each spatial point is regarded as a nonlinear oscillatorand the onset of wave turbulence is the point where the oscillators lose phase synchronization.The authors use an extremely sensitive complex-order parameter to estimate the threshold of weakturbulence and perform a Lyapunov analysis leading to the detection of the so-called blowoutbifurcation.

AB - In this paper the authors analyze the onset of the wave turbulence in the spatially extended threewaveinteracting model by using the concept of synchronization. In order to work with a setof ordinary differential equations, they make a pseudo-spectral decomposition of the wave fieldand identify the onset of wave turbulence as the excitation of spatial modes in the presence ofunderlying temporally chaotic dynamics. Each spatial point is regarded as a nonlinear oscillatorand the onset of wave turbulence is the point where the oscillators lose phase synchronization.The authors use an extremely sensitive complex-order parameter to estimate the threshold of weakturbulence and perform a Lyapunov analysis leading to the detection of the so-called blowoutbifurcation.

KW - Synchronization of chaos

KW - onset of turbulence

KW - wave turbulence

UR - http://hdl.handle.net/10447/103248

M3 - Review article

VL - 2013

JO - MATHEMATICAL REVIEWS

JF - MATHEMATICAL REVIEWS

SN - 0025-5629

ER -