Three-Dimensional Waves in Excitable Reaction-Diffusion Systems: the Eikonal Approximation
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There is a wealth of experimental observation on pattern formation in three dimensional Belousov-Zhabotinsky (BZ) reagent as documented by Welsh [1, 2] and Winfree . The diversity of wave forms evolving in the reagent highlights the complexity of the task faced by theoreticians working within the framework of the full reaction-diffusion (R-D) equations with excitable kinetics. This points to the need for developing analytically tractable, abbreviated models which will at least capture the geometry of the wave forms. An approach that offers considerable scope for generalization to three-dimensional R-D systems is a geometric theory (the eikonal method) proposed by Keener  and Zykov  in the context of spiral waves on a plane.
KeywordsWave Form Spiral Wave Eikonal Equation Eikonal Approximation Helical Surface
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