Drift laws for spiral waves on curved anisotropic surfaces

Hans Dierckx, Evelien Brisard, Henri Verschelde, and Alexander V. Panfilov
Phys. Rev. E 88, 012908 – Published 19 July 2013

Abstract

Rotating spiral waves organize spatial patterns in chemical, physical, and biological excitable systems. Factors affecting their dynamics, such as spatiotemporal drift, are of great interest for particular applications. Here, we propose a quantitative description for spiral wave dynamics on curved surfaces which shows that for a wide class of systems, including the Belousov-Zhabotinsky reaction and anisotropic cardiac tissue, the Ricci curvature scalar of the surface is the main determinant of spiral wave drift. The theory provides explicit equations for spiral wave drift direction, drift velocity, and the period of rotation. Depending on the parameters, the drift can be directed to the regions of either maximal or minimal Ricci scalar curvature, which was verified by direct numerical simulations.

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  • Received 23 January 2013

DOI:https://doi.org/10.1103/PhysRevE.88.012908

©2013 American Physical Society

Authors & Affiliations

Hans Dierckx*, Evelien Brisard, Henri Verschelde, and Alexander V. Panfilov

  • Department of Mathematical Physics and Astronomy, Ghent University, 9000 Ghent, Belgium

  • *hans.dierckx@ugent.be

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Vol. 88, Iss. 1 — July 2013

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