Characterization of on-off intermittency

Heagy, James F.; Platt, Nathan; Hammel, SM

doi:10.1103/physreve.49.1140

Cited by 423 publications

(270 citation statements)

References 21 publications

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“…[26], while the description of the intermittent dynamics is given in Refs. [27,28,29]. Bursting is observed in the temporal evolution of X t as the stability of the fixed point X = 0 varies.…”

Section: S < S Umentioning

confidence: 99%

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Entropy of seismic electric signals: Analysis in natural time under time reversal

et al. 2006

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Electric signals have been recently recorded at the Earth's surface with amplitudes appreciably larger than those hitherto reported. Their entropy in natural time is smaller than that, S u , of a "uniform" distribution. The same holds for their entropy upon time-reversal. This behavior, as supported by numerical simulations in fBm time series and in an on-off intermittency model, stems from infinitely ranged long range temporal correlations and hence these signals are probably Seismic Electric Signals (critical dynamics). The entropy fluctuations are found to increase upon approaching bursting, which reminds the behavior identifying sudden cardiac death individuals when analysing their electrocardiograms.

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Section: S < S Umentioning

confidence: 99%

“…[28], for A 0 = 0 there is a critical value α c > 1, below which the system asymptotically tends to the fixed point X = 0, without any sustained intermittent bursting.…”

Section: S < S Umentioning

confidence: 99%

Entropy of seismic electric signals: Analysis in natural time under time reversal

et al. 2006

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“…Intermittent behavior is an ubiquitous phenomenon in nonlinear science. Its arousal and main statistical properties have been studied and characterized already since long time ago, and different types of intermittency have been classified as types I-III [1, 2] or on-off intermittency [3,4]. One of the most general and interesting manifestations of the intermittent behavior can be observed near of the boundary of chaotic synchronization regimes.…”

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confidence: 99%

Ring Intermittency in Coupled Chaotic Oscillators at the Boundary of Phase Synchronization

et al. 2006

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A new type of intermittent behavior is described to occur near the boundary of phase synchronization regime of coupled chaotic oscillators. This mechanism, called ring intermittency, arises for sufficiently high initial mismatches in the frequencies of the two coupled systems. The laws for both the distribution and the mean length of the laminar phases versus the coupling strength are analytically deduced. A very good agreement between the theoretical results and the numerically calculated data is shown. We discuss how this mechanism is expected to take place in other relevant physical circumstances. Intermittent behavior is an ubiquitous phenomenon in nonlinear science. Its arousal and main statistical properties have been studied and characterized already since long time ago, and different types of intermittency have been classified as types I-III [1, 2] or on-off intermittency [3,4]. One of the most general and interesting manifestations of the intermittent behavior can be observed near of the boundary of chaotic synchronization regimes. Indeed, close to the threshold parameter values for which the coupled systems show synchronized dynamics, it is observed that the de-synchronization mechanism involves persistent intermittent time intervals during which the synchronized oscillations are interrupted by the non-synchronous behavior. These pre-transitional intermittencies have been described in details for the case of lag synchronization [5,6,7] and for generalized synchronization [8], and their main statistical properties (following those of the on-off intermittency) have been shown to be common to other relevant physical processes.As far as intermittency phenomena near the phase synchronization onset are concerned, two types of intermittent behavior have been observed so far [9,10,11,12], namely the type-I intermittency and the super-long laminar behavior (so called "eyelet intermittency" [13]).In this Letter we report that a new type of intermittent behavior is observed near the phase synchronization boundary of two unidirectionally coupled chaotic oscillators, when the natural frequencies of the two oscillators are sufficiently different from one another. The system under study is represented by a pair of unidirectionally coupled Rössler systems, whose equations read aṡy r , z r )] are the cartesian coordinates of the drive (the response) oscillator, dots stand for temporal derivatives, and ε is a parameter ruling the coupling strength. The other control parameters of Eq. (1) have been set to a = 0.15, p = 0.2, c = 10.0, in analogy with previous studies [14,15]. The ω r -parameter (representing the natural frequency of the response system) has been selected to be ω r = 0.95; the analogous parameter for the drive system has been fixed to ω d = 1.0. For such a choice of parameter values, both chaotic attractors of the drive and response systems are, at zero coupling strength, phase coherent. Furthermore, the boundary of the phase synchronization regime occur around ε c ≈ 0.124.The instantaneous phase of the ch...

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“…Its arousal and main statistical properties have been studied and characterized already since long time ago, and different types of intermittency have been classified as types I-III [1,2], on-off intermittency [3,4,5,6], eyelet intermittency [7,8,9] and ring intermittency [10].…”

Section: Introductionmentioning

confidence: 99%

Length distribution of laminar phases for type-I intermittency in the presence of noise

Hramov

Короновский²,

Kurovskaya³

et al. 2007

Phys. Rev. E

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We consider a type of intermittent behavior that occurs as the result of the interplay between dynamical mechanisms giving rise to type-I intermittency and random dynamics. We analytically deduce the laws for the distribution of the laminar phases, with the law for the mean length of the laminar phases versus the critical parameter deduced earlier [PRE 62 (2000) 6304] being the corollary fact of the developed theory. We find a very good agreement between the theoretical predictions and the data obtained by means of both the experimental study and numerical calculations. We discuss also how this mechanism is expected to take place in other relevant physical circumstances.

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Characterization of on-off intermittency

Cited by 423 publications

References 21 publications

Entropy of seismic electric signals: Analysis in natural time under time reversal

Entropy of seismic electric signals: Analysis in natural time under time reversal

Ring Intermittency in Coupled Chaotic Oscillators at the Boundary of Phase Synchronization

Length distribution of laminar phases for type-I intermittency in the presence of noise

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