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Nonlinear Sciences > Pattern Formation and Solitons

arXiv:1412.4731 (nlin)
[Submitted on 15 Dec 2014 (v1), last revised 2 Jun 2015 (this version, v4)]

Title:Unstable Spiral Waves and Local Euclidean Symmetry in a Model of Cardiac Tissue

Authors:Christopher D. Marcotte, Roman O. Grigoriev
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Abstract:This paper investigates the properties of unstable single-spiral wave solutions arising in the Karma model of two-dimensional cardiac tissue. In particular, we discuss how such solutions can be computed numerically on domains of arbitrary shape and study how their stability, rotational frequency, and spatial drift depend on the size of the domain as well as the position of the spiral core with respect to the boundaries. We also discuss how the breaking of local Euclidean symmetry due to finite size effects as well as the spatial discretization of the model is reflected in the structure and dynamics of spiral waves. This analysis allows identification of a self-sustaining process responsible for maintaining the state of spiral chaos featuring multiple interacting spirals.
Comments: 17 pages, 14 figures
Subjects: Pattern Formation and Solitons (nlin.PS)
Cite as: arXiv:1412.4731 [nlin.PS]
  (or arXiv:1412.4731v4 [nlin.PS] for this version)
  https://doi.org/10.48550/arXiv.1412.4731
Related DOI: https://doi.org/10.1063/1.4922596

Submission history

From: Christopher Marcotte [view email]
[v1] Mon, 15 Dec 2014 19:24:09 UTC (3,374 KB)
[v2] Tue, 16 Dec 2014 16:20:56 UTC (3,375 KB)
[v3] Wed, 7 Jan 2015 15:47:30 UTC (1,118 KB)
[v4] Tue, 2 Jun 2015 19:25:52 UTC (1,075 KB)
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