Arnold Diffusion, Ergodicity and Intermittency in a Coupled Standard Mapping

2020 ◽  
pp. 647-652
Author(s):  
Kunihiko Kaneko ◽  
Richard J. Bagley
1985 ◽  
Vol 110 (9) ◽  
pp. 435-440 ◽  
Author(s):  
Kunihiko Kaneko ◽  
Richard J. Bagley

2013 ◽  
Vol 251 ◽  
pp. 19-38 ◽  
Author(s):  
C. Efthymiopoulos ◽  
M. Harsoula
Keyword(s):  

1984 ◽  
Vol 31 (8) ◽  
pp. 673-688 ◽  
Author(s):  
F. Salam ◽  
J. Marsden ◽  
P. Varaiya

1986 ◽  
Vol 39 (5) ◽  
pp. 395-399
Author(s):  
L. D. Pustyl'nikov

2019 ◽  
Vol 30 (3) ◽  
pp. 851-901
Author(s):  
Massimiliano Guzzo ◽  
Christos Efthymiopoulos ◽  
Rocío I. Paez

2003 ◽  
Vol 285 (4) ◽  
pp. H1705-H1719 ◽  
Author(s):  
Alan Kadish ◽  
David Johnson ◽  
Willie Choe ◽  
Jeffrey Goldberger ◽  
George Horvath

Recent studies have demonstrated that fibrillatory rhythms are not random phenomena but have definable patterns. However, standard mapping techniques may have limitations in their ability to identify the organization of fibrillation. The purpose of this study was to develop and apply a method, “ensemble vector mapping,” for characterizing the spatiotemporal organization of fibrillation. Ventricular fibrillation was induced by burst pacing in normal mongrel dogs. In a separate protocol, atrial fibrillation was induced by epicardial aconitine application. Epicardial electrograms were recorded from a 112-electrode plaque array using a computerized mapping system. Vectors were created by summing orthogonal bipolar electrograms. The magnitude of the vectors was transformed using a logarithmic function, integrated over time, and normalized for local electrogram amplitude to produce an “ensemble vector” index whose magnitude is high when beat-to-beat activation direction is consistent and low when activation direction is variable. The mean index was 137 ± 36 mV/s during ventricular pacing at a cycle length of 300 ms but only 39 ± 23 mV/s during ventricular fibrillation ( P < 0.001). The ensemble vector index was also lower during atrial fibrillation (60 ± 54 mV/s) than during atrial pacing (115 ± 27 mV/s, P < 0.01 vs. atrial fibrillation) but not as low as during ventricular fibrillation ( P < 0.05, atrial vs. ventricular fibrillation). The index was also capable of distinguishing atrial tachycardia from atrial fibrillation. Ensemble vector mapping produces an objective assessment of the consistency of myocardial activation during fibrillation. The consistency of activation direction differs in different models of fibrillation and is higher during atrial than ventricular fibrillation. This technique has the potential to rapidly characterize repetitive activation patterns in fibrillatory rhythms and may help distinguish among different characteristics of fibrillatory rhythms.


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