Abstract
Many theoretical and experimental studies indicate that a propagation block represents an important factor in spiral wave initiation in excitable media. The analytical and numerical results we obtained for a generic two-component reaction-diffusion system demonstrate quantitative conditions for the propagation block in a one-dimensional and a two-dimensional medium due to a sharp spatial increase of the medium's excitability or the coupling strength above a certain critical value. Here, we prove that this critical value strongly depends on the medium parameters and the geometry of the inhomogeneity. For an exemplary two-dimensional medium, we show how the propagation block can be used to initiate spiral waves by a specific choice of the size and shape of the medium's inhomogeneity.
Highlights
Spiral waves are typical spatio-temporal patterns which have been observed in a broad spectrum of excitable media including the colonies of Dictyostelium discoideum,1 the chemical Belousov-Zhabotinsky reaction,2 the heart muscle,3 the eye retina,4 the CO oxidation on platinum single crystal surface,5 and many others
The mechanical contraction of cardiac muscle is driven by a periodic electrical activation which propagates through the tissue as excitation waves
We took an initial step in this direction,12 where we demonstrated an important role of a fast propagation region (FPR) in the spiral wave creation
Summary
Spiral waves are typical spatio-temporal patterns which have been observed in a broad spectrum of excitable media including the colonies of Dictyostelium discoideum, the chemical Belousov-Zhabotinsky reaction, the heart muscle, the eye retina, the CO oxidation on platinum single crystal surface, and many others. There are many ways to create a phase change point that is a necessary condition to initiate spiral waves.. If the medium’s refractoriness is nonuniform in space, a secondary excitation applied at a suitable time will be blocked, creating phase change points. We took an initial step in this direction, where we demonstrated an important role of a fast propagation region (FPR) in the spiral wave creation. Based on these results, we demonstrate how FPR can be formed to initiate spiral waves in a two-dimensional excitable medium. It can be seen that for all parameters of the model Eqs. (1)–(4) fixed except for , there exists a maximum value of above which propagating pulse solution does not exist
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