Strange attractors in weakly turbulent Couette-Taylor flow

Brandstäter, A.; Swinney, Harry L.

doi:10.1103/physreva.35.2207

Cited by 219 publications

(116 citation statements)

References 26 publications

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“…Thus, ring-like structures around which the state point precesses (see below), such as observed in our fibrillation data, suggest chaos that has arisen from quasiperiodicity. Similar ring-like structures have been observed in other physical systems undergoing transitions from quasiperiodicity to chaos, such as the transition to turbulence in fluids (34)(35)(36) and to chaos in electronic materials (37). In addition, mathematical models, which, like cardiac conduction, are governed by reaction-diffusion equations in excitable media, have been shown to undergo transitions to spatio-temporal chaos via a quasiperiodic route (39,40).…”

Section: Discussionsupporting

confidence: 62%

“…This was shown to be mathematically impossible by Ruelle, Takens, and Newhouse (32,33), who proved that a system containing three or more coupled oscillations is unstable. Their predictions were confirmed experimentally by the elegant fluid dynamics studies of Swinney and others (34)(35)(36), and have been extended to other systems such as electronic materials (37).…”

Section: Discussionmentioning

confidence: 73%

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Quasiperiodicity and chaos in cardiac fibrillation.

et al. 1997

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In cardiac fibrillation, disorganized waves of electrical activity meander through the heart, and coherent contractile function is lost. We studied fibrillation in three stationary forms: in human chronic atrial fibrillation, in a stabilized form of canine ventricular fibrillation, and in fibrillationlike activity in thin sheets of canine and human ventricular tissue in vitro. We also created a computer model of fibrillation. In all four studies, evidence indicated that fibrillation arose through a quasiperiodic stage of period and amplitude modulation, thus exemplifying the "quasiperiodic transition to chaos" first suggested by Ruelle and Takens. This suggests that fibrillation is a form of spatio-temporal chaos, a finding that implies new therapeutic approaches. ( J. Clin. Invest. 1997. 99:305-314.)

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Section: Discussionsupporting

confidence: 62%

Section: Discussionmentioning

confidence: 73%

Quasiperiodicity and chaos in cardiac fibrillation.

et al. 1997

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“…Mathematicians predicted in 1971 that systems consisting of three or more independent coupled oscillations would be unstable, and degenerate into chaos (5). Since their mathematical demonstration, experimentalists have shown that such quasiperiodic transitions to chaos do occur in a number of systems, such as the transition to turbulence in fluids (26). Recently, our group presented evidence for quasiperiodic transitions to chaos in cardiac fibrillation (4).…”

Section: Discussionmentioning

confidence: 96%

Spatiotemporal complexity of ventricular fibrillation revealed by tissue mass reduction in isolated swine right ventricle. Further evidence for the quasiperiodic route to chaos hypothesis.

Kim¹,

et al. 1997

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We have presented evidence that ventricular fibrillation is deterministic chaos arising from quasiperiodicity. The purpose of this study was to determine whether the transition from chaos (ventricular fibrillation, VF) to periodicity (ventricular tachycardia) through quasiperiodicity could be produced by the progressive reduction of tissue mass. In isolated and perfused swine right ventricular free wall, recording of single cell transmembrane potentials and simultaneous mapping (477 bipolar electrodes, 1.6 mm resolution) were performed. The tissue mass was then progressively reduced by sequential cutting. All isolated tissues fibrillated spontaneously. The critical mass to sustain VF was 19.9 Ϯ 4.2 g. As tissue mass was decreased, the number of wave fronts decreased, the life-span of reentrant wave fronts increased, and the cycle length, the diastolic interval, and the duration of action potential lengthened. There was a parallel decrease in the dynamical complexity of VF as measured by Kolmogorov entropy and Poincaré plots. A period of quasiperiodicity became more evident before the conversion from VF (chaos) to a more regular arrhythmia (periodicity). In conclusion, a decrease in the number of wave fronts in ventricular fibrillation by tissue mass reduction causes a transition from chaotic to periodic dynamics via the quasiperiodic route.

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“…3C) shows a dramatic change including significant spreading of the orbits throughout the phase map. Spreading of attractor orbits of chaotic flow has been observed experimentally in the multiple periodic-to-chaotic regime transitions in Taylor-Couette flows (3,22). The phenomenon is also evident in classical dynamical systems attractors such as the Rössler attractor and the differential-delay equation (Mackey-Glass (4).…”

Section: Resultsmentioning

confidence: 84%

“…2A). Periodic windows sandwiched between aperiodic regimes have been observed experimentally in, for example, the Belousov-Zabotinsky reaction (21) and in moderately high Reynolds number TaylorCouette flow (3,16,22). They are also well known as in mathematical models with one-dimensional mappings such as the Rössler attractor (4).…”

Section: Resultsmentioning

confidence: 98%

Electric fields yield chaos in microflows

Posner

Pérez

Santiago

2012

Proc. Natl. Acad. Sci. U.S.A.

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We present an investigation of chaotic dynamics of a low Reynolds number electrokinetic flow. Electrokinetic flows arise due to couplings of electric fields and electric double layers. In these flows, applied (steady) electric fields can couple with ionic conductivity gradients outside electric double layers to produce flow instabilities. The threshold of these instabilities is controlled by an electric Rayleigh number, Ra e . As Ra e increases monotonically, we show here flow dynamics can transition from steady state to a timedependent periodic state and then to an aperiodic, chaotic state. Interestingly, further monotonic increase of Ra e shows a transition back to a well-ordered state, followed by a second transition to a chaotic state. Temporal power spectra and time-delay phase maps of low dimensional attractors graphically depict the sequence between periodic and chaotic states. To our knowledge, this is a unique report of a low Reynolds number flow with such a sequence of periodic-to-aperiodic transitions. Also unique is a report of strange attractors triggered and sustained through electric fluid body forces.fluid mechanics | electrohydrodynamics | electrokinetic instability

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Strange attractors in weakly turbulent Couette-Taylor flow

Cited by 219 publications

References 26 publications

Quasiperiodicity and chaos in cardiac fibrillation.

Quasiperiodicity and chaos in cardiac fibrillation.

Spatiotemporal complexity of ventricular fibrillation revealed by tissue mass reduction in isolated swine right ventricle. Further evidence for the quasiperiodic route to chaos hypothesis.

Electric fields yield chaos in microflows

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