On the Implementation of the 0–1 Test for Chaos

Gottwald, Georg A.; Melbourne, Ian

doi:10.1137/080718851

Cited by 404 publications

(361 citation statements)

References 23 publications

(51 reference statements)

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“…1 (in present calculations n ¼ n max ¼ 150 while N ¼ 1350) we obtain the corresponding values of K c for a chosen value of c. Note, our choice of n max and N limits (in Eqs. 4,5) is consistent with that proposed by Gottwald and Melbourne [34,35,40]. N; n max !…”

Section: The 0-1 Testsupporting

confidence: 78%

“…If c is badly chosen, it could resonate with the excitation frequency or its super-or sub-harmonics. In the 0-1 test, regular motion would yield an expanding behaviour in the (p, q)-plane [34] and the corresponding M c ðnÞ has an asymptotic growth rate even for a regular system. The disadvantage of the test, its strong dependence on the chosen parameter c, can be overcome by a proposed modification.…”

Section: The 0-1 Testmentioning

confidence: 99%

“…The disadvantage of the test, its strong dependence on the chosen parameter c, can be overcome by a proposed modification. Gottwald and Melbourne [34,36,37] suggested randomly chosen values of c are taken and the median of the corresponding K c -values are computed.…”

Section: The 0-1 Testmentioning

confidence: 99%

See 2 more Smart Citations

Regular and chaotic vibration in a piezoelectric energy harvester

2015

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We examine regular and chaotic responses of a vibrational energy harvester composed of a vertical beam and a tip mass. The beam is excited horizontally by a harmonic inertial force while mechanical vibrational energy is converted to electrical power through a piezoelectric patch. The mechanical resonator can be described by single or double well potentials depending on the gravity force from the tip mass. By changing the tip mass we examine bifurcations from single well oscillations, to regular and chaotic vibrations between the potential wells. The appearance of chaotic responses in the energy harvesting system is illustrated by the bifurcation diagram, the corresponding Fourier spectra, the phase portraits, and is confirmed by the 0-1 test. The appearance of chaotic vibrations reduces the level of harvested energy.

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Section: The 0-1 Testsupporting

confidence: 78%

Section: The 0-1 Testmentioning

confidence: 99%

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Regular and chaotic vibration in a piezoelectric energy harvester

2015

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“…Of great importance in this direction was also the algorithm proposed by Benettin and co-workers [3,4,5] regarding the computation of the full spectrum of Lyapunov exponents (LEs) associated with the time evolution of deviation vectors from a reference orbit, which applies to dynamical systems of arbitrary dimension. More recently, other related methods have been proposed in the literature, like the "Fast Lyapunov Indicator" [6,7] and the "Mean Exponential Growth of Nearby Orbits" (MEGNO) [8,9], while there have also been approaches focusing on the time series constructed by the coordinates of each orbit, like the "Frequency Map Analysis" [10,11,12] and the "0-1" test [13,14,15]. Interesting accounts of these methods can be found in [16], as well as in a more recent review paper [5].…”

Section: Introductionmentioning

confidence: 99%

Interplay between chaotic and regular motion in a time-dependent barred galaxy model

Manos¹,

Bountis²,

Skokos³

2013

J. Phys. A: Math. Theor.

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Abstract. We study the distinction and quantification of chaotic and regular motion in a time-dependent Hamiltonian barred galaxy model. Recently, a strong correlation was found between the strength of the bar and the presence of chaotic motion in this system, as models with relatively strong bars were shown to exhibit stronger chaotic behavior compared to those having a weaker bar component. Here, we attempt to further explore this connection by studying the interplay between chaotic and regular behavior of star orbits when the parameters of the model evolve in time. This happens for example when one introduces linear time dependence in the mass parameters of the model to mimic, in some general sense, the effect of self-consistent interactions of the actual N-body problem. We thus observe, in this simple time-dependent model also, that the increase of the bar's mass leads to an increase of the system's chaoticity. We propose a new way of using the Generalized Alignment Index (GALI) method as a reliable criterion to estimate the relative fraction of chaotic vs. regular orbits in such time-dependent potentials, which proves to be much more efficient than the computation of Lyapunov exponents. In particular, GALI is able to capture subtle changes in the nature of an orbit (or ensemble of orbits) even for relatively small time intervals, which makes it ideal for detecting dynamical transitions in time-dependent systems.PACS numbers: 95.10. Fh, 05.45.Ac, 05.45.Pq, 98.62.Ck, 98.62.Dm, 98.62.Hr

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“…Between one fifth and one quarter of Compound networks actually showed stable, non-oscillating dynamic values of W. For 19 (4%) of the networks, we found evidence of aperiodicity. Four of these aperiodic networks passed the 0-1 test for chaos [41,42] with 10 replicate runs giving R values>0.99. The longest repeating period we observed was 210 iterations.…”

Section: Oscillation Periodmentioning

confidence: 99%