A Geometrical Theory for Spiral Waves in Excitable Media
SIAM Journal on Applied Mathematics1986Vol. 46(6), pp. 1039–1056
Citations Over TimeTop 10% of 1986 papers
Abstract
In this paper, we develop a geometrical theory for waves in excitable reacting media. Using singular perturbation arguments and dispersion of traveling plane wave trains, we derive an approximate theory of wave front propagation which has strong resemblance to the geometrical diffraction theory of high frequency waves in hyperbolic systems, governed by the eikonal equation. Using this theory, we study the effect of curvature on waves in excitable media, specifically, rotating spiral patterns in planar regions. From this theory we are able to determine the frequency and wavelength for spiral patterns in excitable, nonoscillatory media.
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