Chaotic transients in spatially extended systems

Tél, Tamás; Lai, Ying Cheng

doi:10.1016/j.physrep.2008.01.001

Cited by 128 publications

(117 citation statements)

References 110 publications

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“…The very fact that the transient is Lyapunov-stable makes it substantially different from the chaotic transients that have been often found and attributed to the existence of some chaotic saddle of high dimensionality [8]. This is all the way more surprising once we notice that the "transient" dynamics is far from regular.…”

Section: Definition and Characterization Of Stable Chaosmentioning

confidence: 77%

“…One might therefore think of using tools and ideas developed for the characterization of transients such as those extensively discussed in the nice review by Tèl and Lai [8]. One must however distinguish between SC and standard chaotic transients (for a seminal paper on the subject, see [9]).…”

Section: Introductionmentioning

confidence: 99%

“…Nevertheless, we suspect that a possible common property of chaotic transients and SC is the presence of a strange repeller. In fact, chaotic transients are almost by definition the manifestation of trajectories evolving in the vicinity of a repeller, possibly characterized by a small escape rate [8,10]. This property seems to clash with the absense of unstable orbits in most of the models exhibiting SC.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Nonlinear Dynamics and Chaos: Advances and Perspectives

Thiel¹,

Kurths²,

Romano³

et al. 2010

Understanding Complex Systems

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Abstract. Stable chaos is a generalization of the chaotic behaviour exhibited by cellular automata to continuous-variable systems and it owes its name to an underlying irregular and yet linearly stable dynamics. In this review we discuss analogies and differences with the usual deterministic chaos and introduce several tools for its characterization. Some examples of transitions from ordered behavior to stable chaos are also analyzed to further clarify the underlying dynamical properties. Finally, two models are specifically discussed: the diatomic hard-point gas chain and a network of globally coupled neurons.

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Section: Definition and Characterization Of Stable Chaosmentioning

confidence: 77%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Nonlinear Dynamics and Chaos: Advances and Perspectives

Thiel¹,

Kurths²,

Romano³

et al. 2010

Understanding Complex Systems

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show abstract

“…3(b), indicating a complete transient phenomenon, as also found in other spatially extended systems. 27 For Re > 660, E k increases continuously (see Fig. 3(a)) and the ITB "seed" can extend to a very long turbulent band as shown by the visualization in Fig.…”

Section: -mentioning

confidence: 94%

Turbulent bands in plane-Poiseuille flow at moderate Reynolds numbers

et al. 2015

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In this letter, we show via numerical simulations that the typical flow structures appearing in transitional channel flows at moderate Reynolds numbers are not spots but isolated turbulent bands, which have much longer lifetimes than the spots. Localized perturbations can evolve into isolated turbulent bands by continuously growing obliquely when the Reynolds number is larger than 660. However, interactions with other bands and local perturbations cause band breaking and decay. The competition between the band extension and breaking does not lead to a sustained turbulence until Re becomes larger than about 1000. Above this critical value, the bands split, providing an effective mechanism for turbulence spreading.

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“…Chaotic saddles are nonattracting coherent structures responsible for temporary chaos ubiquitous in spatially extended systems such as the advection-reaction-diffusion systems, excitable media, complex networks, and turbulent shear flows [1]. Experimental evidence of chaotic saddles has been obtained in lasers [2] and pipe flows [3].…”

mentioning

confidence: 99%

Amplitude-Phase Synchronization at the Onset of Permanent Spatiotemporal Chaos

Chian

Miranda²,

Rempel³

et al. 2010

Phys. Rev. Lett.

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Amplitude and phase synchronization due to multiscale interactions in chaotic saddles at the onset of permanent spatiotemporal chaos is analyzed using the Fourier-Lyapunov representation. By computing the power-phase spectral entropy and the time-averaged power-phase spectra, we show that the laminar (bursty) states in the on-off spatiotemporal intermittency correspond, respectively, to the nonattracting coherent structures with higher (lower) degrees of amplitude-phase synchronization across spatial scales.

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Chaotic transients in spatially extended systems

Cited by 128 publications

References 110 publications

Nonlinear Dynamics and Chaos: Advances and Perspectives

Nonlinear Dynamics and Chaos: Advances and Perspectives

Turbulent bands in plane-Poiseuille flow at moderate Reynolds numbers

Amplitude-Phase Synchronization at the Onset of Permanent Spatiotemporal Chaos

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