Experimental observation of crisis-induced intermittency and its critical exponent

Ditto, William L.; Rauseo, S. N.; Cawley, Robert; Grebogi, Celso; Hsu, Guan-Hsong; Kostelich, Eric J.; Ott, Edward; Savage, H. T.; Segnan, R.; Spano, Mark L.; Yorke, James A.

doi:10.1103/physrevlett.63.923

Cited by 118 publications

(29 citation statements)

References 13 publications

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“…However, the least squares fit to the data in Fig. 4 shows that the half-life / Re c ÿ Re ÿ10:02 , which in dynamical systems theory is a generic feature associated with transient behavior where an attractor loses stability at a crisis [5,6]. In maps and low-dimensional dynamical systems the exponent has been found to be less than 1 but the qualitative features are similar to those uncovered here.…”

Section: Prl 96 094501 (2006) P H Y S I C a L R E V I E W L E T T E supporting

confidence: 70%

“…Therefore, we have devised a novel experiment to investigate the reverse transition, i.e., the change from turbulent to laminar flow. The flow can now be considered as a dynamical system where the turbulent attractor loses stability at a crisis as a parameter is changed [5,6]. Exponential decay of the disordered motion is found when the Reynolds number is reduced and, moreover, the observed divergence in the time scales indicates an underlying critical event.…”

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confidence: 99%

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Decay of Turbulence in Pipe Flow

2006

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Section: Prl 96 094501 (2006) P H Y S I C a L R E V I E W L E T T E supporting

confidence: 70%

mentioning

confidence: 99%

Decay of Turbulence in Pipe Flow

2006

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“…Examples of numerical analysis of partial differential equations which exhibit low-dimensional chaos include a model for the nonlinear evolution of low-frequency magnetohydrodynamic oscillations in plasmas, 43 a generic model for the propagation of nonlinear waves in forced, spatially extended medium, 44 and a model for semiconductor devices. 45 Experimental examples include a magnetoelastic ribbon, 46 electronic circuits, 47 a dripping faucet, 48 experiments with air bubbles, 49 and lasers. 50 …”

Section: Discussionmentioning

confidence: 99%

Analysis of chaotic saddles in high-dimensional dynamical systems: The Kuramoto–Sivashinsky equation

Rempel

Chian

Macau

et al. 2004

Chaos: An Interdisciplinary Journal of Nonlinear Science

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This paper presents a methodology to study the role played by nonattracting chaotic sets called chaotic saddles in chaotic transitions of high-dimensional dynamical systems. Our methodology is applied to the Kuramoto-Sivashinsky equation, a reaction-diffusion partial differential equation. The paper describes a novel technique that uses the stable manifold of a chaotic saddle to characterize the homoclinic tangency responsible for an interior crisis, a chaotic transition that results in the enlargement of a chaotic attractor. The numerical techniques explained here are important to improve the understanding of the connection between low-dimensional chaotic systems and spatiotemporal systems which exhibit temporal chaos and spatial coherence. © 2004 American Institute of Physics. ͓DOI: 10.1063/1.1759297͔In the past decades chaos theory has been revealed as a powerful way to explain the physics of low-dimensional dynamical systems, that is, dynamical systems with a small number of state variables. However, most problems of practical interest in physics and engineering are described by partial differential equations "PDEs…, and it is still unclear in which situations the physical mechanisms responsible for the onset of chaos in low-dimensional systems are applicable to systems described by PDEs. Several authors have tried to develop a dynamical systems theory for high-dimensional dynamical systems, frequently described by sets of coupled ordinary differential equations obtained as approximations to the original PDEs. 1-7 The simplest approach consists in first ''borrowing'' the tools developed for low-dimensional dynamical systems and applying them to spatially extended systems in regimes that display characteristics of lowdimensional chaos. Then, it is possible to develop the tools to be used in more complex regimes. In this paper we try to improve the understanding of the connection between low-dimensional chaotic systems and a certain class of spatiotemporal systems: the one that exhibits temporal chaos and spatial coherence. We focus on the development of a methodology to study the role played by nonattracting chaotic sets called chaotic saddles in chaotic transitions of high-dimensional dynamical systems.

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“…For a detailed discussion on the structure of the chaotic attractor, we here address the reader to Ref. [145].…”

Section: Control Of Chaos With Ogy Methodsmentioning

confidence: 99%