Experimental observation of strange nonchaotic attractors in a driven excitable system

Ruiz, Guiomar; Parmananda, P.

doi:10.1016/j.physleta.2007.03.053

Cited by 26 publications

(12 citation statements)

References 13 publications

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“…SNAs have been reported in many physical systems such as the quasiperiodically forced pendulum [12], biological oscillators [13], and quantum particles in quasiperiodic potentials [14], which are also related to the Anderson localization in the Schrödinger equation [15]. Also, these exotic attractors were confirmed by an experiment consisting of a quasiperiodically forced, buckled, magnetoelastic ribbon [16], in analog simulations of a multistable potential [17], neon glow discharge experiment [18], chemical oscillations [19] and various electronic circuits [20,21]. SNAs can be quantitatively characterized by a variety of methods, including the estimation of Lyapunov exponents and fractal dimension [11,22,23] and spectral properties [24,25].…”

Section: Introductionmentioning

confidence: 86%

Applicability of 0-1 test for strange nonchaotic attractors

Gopal

Venkatesan²,

Lakshmanan

2013

Chaos: An Interdisciplinary Journal of Nonlinear Science

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We show that the recently introduced 0-1 test can successfully distinguish between strange nonchaotic attractors (SNAs) and periodic/quasiperiodic/chaotic attractors, by suitably choosing the arbitrary parameter associated with the translation variables in terms of the golden mean number which avoids resonance with the quasiperiodic force. We further characterize the transition from quasiperiodic to chaotic motion via SNAs in terms of the 0-1 test. We demonstrate that the test helps to detect different dynamical transitions to SNAs from quasiperiodic attractor or the transitions from SNAs to chaos. We illustrate the performance of the 0-1 test in detecting transitions to SNAs in quasiperiodically forced logistic map, cubic map, and Duffing oscillator.

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Section: Introductionmentioning

confidence: 86%

Applicability of 0-1 test for strange nonchaotic attractors

Gopal

Venkatesan²,

Lakshmanan

2013

Chaos: An Interdisciplinary Journal of Nonlinear Science

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“…The strange nonchaotic signatures of variable stars like KIC 5520878 may elucidate phenomena like the Eddington valve mechanism [31] thought to underlie their pulsations: variations in the opacity of the star might quasiperiodically modulate the normal hydrostatic balance between pressure outward and gravity inward, thereby generating light curves somewhere between order and chaos that the best models will need to reproduce. Strange nonchaotic attractors have been observed in laboratory experiments involving magnetoelastic ribbons [12], electrochemical cells [32], electronic circuits [33], and a neon glow discharge [34], but never before in non-experiments in nature. The pulsating star KIC 5520878 may be the first strange nonchaotic dynamical system observed in the wild.…”

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confidence: 99%

Strange Nonchaotic Stars

et al. 2015

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The unprecedented light curves of the Kepler space telescope document how the brightness of some stars pulsates at primary and secondary frequencies whose ratios are near the golden mean, the most irrational number. A nonlinear dynamical system driven by an irrational ratio of frequencies generically exhibits a strange but nonchaotic attractor. For Kepler 's "golden" stars, we present evidence of the first observation of strange nonchaotic dynamics in nature outside the laboratory. This discovery could aid the classification and detailed modeling of variable stars.

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“…However, related to the strange geometry of SNAs, trajectories x(t) have nonexponential sensitivity on initial phases θ(0) [36][37][38][39] or on parameter values of the systems [40]. SNAs have been observed in many laboratory experiments [35,[41][42][43][44][45][46] but very rarely in nature so far. Linder et al show that the brightness changes of some RRc Lyrae stars have nonchaotic and fractal properties of SNAs [47].Recently, the authors of this paper showed that several models of glacial cycles exhibit SNAs [27,28].…”

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confidence: 99%

Bifurcations and strange nonchaotic attractors in a phase oscillator model of glacial–interglacial cycles

Mitsui

Crucifix

Aihara

2015

Physica D: Nonlinear Phenomena

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Glacial-interglacial cycles are large variations in continental ice mass and greenhouse gases, which have dominated climate variability over the Quaternary. The dominant periodicity of the cycles is ∼40 kyr before the socalled middle Pleistocene transition between ∼1.2 and ∼0.7 Myr ago, and it is ∼100 kyr after the transition. In this paper, the dynamics of glacialinterglacial cycles are investigated using a phase oscillator model forced by the time-varying incoming solar radiation (insolation). We analyze the bifurcations of the system and show that strange nonchaotic attractors appear through nonsmooth saddle-node bifurcations of tori. The bifurcation analysis indicates that mode-locking is likely to occur for the 41 kyr glacial cycles but not likely for the 100 kyr glacial cycles. The sequence of mode-locked 41 kyr cycles is robust to small parameter changes. However, the sequence of 100 kyr glacial cycles can be sensitive to parameter changes when the system has a strange nonchaotic attractor.

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Experimental observation of strange nonchaotic attractors in a driven excitable system

Cited by 26 publications

References 13 publications

Applicability of 0-1 test for strange nonchaotic attractors

Applicability of 0-1 test for strange nonchaotic attractors

Strange Nonchaotic Stars

Bifurcations and strange nonchaotic attractors in a phase oscillator model of glacial–interglacial cycles

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