Collapse of Spatiotemporal Chaos

Wackerbauer, Renate; Showalter, Kenneth

doi:10.1103/physrevlett.91.174103

Cited by 35 publications

(21 citation statements)

References 21 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The fundamental question of interest is whether there is a critical Reynolds number, or equivalently domain length, beyond which spatio-temporal chaos becomes persistent, i.e., beyond which spatio-temporal chaos becomes an attractor of the system. In other systems of this type, such as reaction-diffusion systems [19,20], detailed simulations have revealed that observed spatio-temporal chaos in one spatial dimension has a lifetime that increases exponentially with domain length but apparently remains finite for all domain lengths. In these systems spatio-temporal chaos appears therefore to be a super-transient and is never an attractor.…”

Section: Transient Spatiotemporal Chaos In the Complexmentioning

confidence: 99%

Transient spatio-temporal chaos in the complex Ginzburg–Landau equation on long domains

Houghton¹,

Knobloch²,

Tobias³

et al. 2010

Physics Letters A

View full text Add to dashboard Cite

Section: Transient Spatiotemporal Chaos In the Complexmentioning

confidence: 99%

Transient spatio-temporal chaos in the complex Ginzburg–Landau equation on long domains

Houghton¹,

Knobloch²,

Tobias³

et al. 2010

Physics Letters A

View full text Add to dashboard Cite

“…Previous simulation studies have indicated that spatiotemporal chaos in generic one-and two-dimensional reaction-diffusion systems [44][45][46] and electrical turbulence in cardiac tissue 35 are often transient states. Therefore, we have checked the lifetimes of electrical turbulence in the absence of defibrillation and with initial conditions generated as described in section II E. With no-flux boundaries, both the (LR) and the (TT) model exhibit rather short spatiotemporal chaos while the turbulence in the (FK) model is quite persistent, see fig.…”

Section: A Electrical Turbulencementioning

confidence: 99%

Control of electrical turbulence by periodic excitation of cardiac tissue

Buran

Bär

Alonso

et al. 2017

Chaos: An Interdisciplinary Journal of Nonlinear Science

View full text Add to dashboard Cite

Electrical turbulence in cardiac tissue is associated with arrhythmias such as the life-threatening ventricular fibrillation. The application of a high-energy electrical shock constitutes an effective defibrillation, but also causes severe side effects. Recent experimental studies have shown that a sequence of low energy electrical far-field pulses is able to terminate fibrillation more gently than a single pulse. During this low-energy antifibrillation pacing (LEAP) only tissue near sufficiently large conduction heterogeneities, such as large coronary arteries, is activated. In order to understand and potentially optimize LEAP, we performed extensive simulations of cardiac tissue perforated by blood vessels. We checked three alternative cellular models that exhibit qualitatively different electrical turbulence. LEAP may operate if and only if the spectrum of this chaotic activity is characterized by a narrow peak around a dominant frequency. For each of 100 initial conditions, we tested different electrical field strengths, pulse shapes, numbers of pulses, and periods between the pulses. It turned out that the optimal period matches the dominant period of the chaotic activity while both over-and underdrive pacing lead to a considerably smaller success probability and higher field strength for reliable defibrillation. An optimal LEAP protocol, which minimizes the required total energy for successful defibrillation, consists of five or six pulses. Compared to a single bi-phasic defibrillation pulse, it reduces the total energy by about 86%, corresponding to an energy reduction of 97 -98% per pulse.PACS numbers: ... Keywords: cardiac modeling, excitable media, defibrillation, low-energy antifibrillation pacing (LEAP)In ventricular fibrillation, the heart is quivering instead of pumping, a condition which leads to cardiac arrest and ultimately to death. This loss of synchronous contraction stems from disorganized electrical activity in the ventricles. Emergency defibrillation is achieved by the application of a strong electrical shock which is accompanied by severe side effects such as tissue damage and trauma. Recently, an alternative treatment using a sequence of low energy pulses has been suggested in which each electrical pulse excites only localized tissue sites at the large heterogeneities -such as blood vessels -instead of the entire tissue. In laboratory experiments in vitro and in vivo, this so-called low-energy antifibrillation pacing (LEAP) with five pulses achieves defibrillation with an energy reduction of 80 -90 % per pulse in comparison with standard single shock treatment. Here, we perform an extensive numerical study of LEAP employing far field pacing at the major blood vessels. We have tested three alternative electrophysiological models that exhibit qualitatively different spatiotemporally chaotic activity. LEAP operates if and only if the spectrum of this chaotic activity is characterized by a narrow peak around a dominant frequency. In this case, a resonant pacing with the same frequency and a ...

show abstract

“…It has been shown that the Hopf-pitchfork bifurcation leads to complicated bifurcations and various solutions in several systems, e.g., Chua's circuit, 102 a modified van der Pol-Duffing oscillator, 103 coupled reaction-diffusion equations, 104 and coupled tunnel diodes. 105 Further, chaotic transients shown in reaction-diffusion systems [23][24][25][26][27][28][29][30][31] occur near another kind of codimension-two bifurcation point: the Turing-Hopf bifurcation point.…”

Section: Introductionmentioning

confidence: 98%

“…4 ) Chaotic transients in coupled map lattices have been extensively studied since then. Further, they have been found in various systems: the Kuramoto-Shivashinsky equation, 5,6 turbulence in shear flow, 7-18 the complex Ginzburg-Landau equation, [19][20][21][22] reaction-diffusion systems, [23][24][25][26][27][28][29][30][31] neural networks, [32][33][34][35][36][37][38] spatially extended ecological systems, [39][40][41][42][43] and complex networks; [44][45][46] see Ref. 1 for review.…”

Section: Introductionmentioning

confidence: 98%

Transient chaotic rotating waves in a ring of unidirectionally coupled symmetric Bonhoeffer-van der Pol oscillators near a codimension-two bifurcation point

Horikawa

Kohno

2012

Chaos: An Interdisciplinary Journal of Nonlinear Science

View full text Add to dashboard Cite

Propagating waves in a ring of unidirectionally coupled symmetric Bonhoeffer-van der Pol (BVP) oscillators were studied. The parameter values of the BVP oscillators were near a codimension-two bifurcation point around which oscillatory, monostable, and bistable states coexist. Bifurcations of periodic, quasiperiodic, and chaotic rotating waves were found in a ring of three oscillators. In rings of large numbers of oscillators with small coupling strength, transient chaotic waves were found and their duration increased exponentially with the number of oscillators. These exponential chaotic transients could be described by a coupled map model derived from the Poincaré map of a ring of three oscillators. The quasiperiodic rotating waves due to the mode interaction near the codimension-two bifurcation point were evidently responsible for the emergence of the transient chaotic rotating waves.

show abstract

Collapse of Spatiotemporal Chaos

Cited by 35 publications

References 21 publications

Transient spatio-temporal chaos in the complex Ginzburg–Landau equation on long domains

Transient spatio-temporal chaos in the complex Ginzburg–Landau equation on long domains

Control of electrical turbulence by periodic excitation of cardiac tissue

Transient chaotic rotating waves in a ring of unidirectionally coupled symmetric Bonhoeffer-van der Pol oscillators near a codimension-two bifurcation point

Contact Info

Product

Resources

About