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Three-Dimensional Waves in Excitable Reaction-Diffusion Systems: the Eikonal Approximation

  • J. Gomatam
  • P. Grindrod
Chapter
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Part of the NATO ASI Series book series (NSSB, volume 244)

Abstract

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 [3]. 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 [4] and Zykov [5] in the context of spiral waves on a plane.

Keywords

Wave Form Spiral Wave Eikonal Equation Eikonal Approximation Helical Surface 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

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Copyright information

© Springer Science+Business Media New York 1991

Authors and Affiliations

  • J. Gomatam
    • 1
  • P. Grindrod
    • 2
  1. 1.Department of MathematicsGlasgow CollegeGlasgowUK
  2. 2.INTERA-ECLHighlands FarmHenley-on-Thames, OxonUK

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