### Abstract

Diffraction of spherical waves by a toroidal obstacle is analysed using the eikonal approximation to the reaction-diffusion equations with excitable kinetics. We demonstrate the existence of two stationary spherical wave segments, one larger and the other smaller than a hemisphere, blocking the hole of the torus. A detailed stability analysis indicates that the former is unstable and the latter is stable. This analysis suggests that the trapping of a spherical wave front by a toroidal obstacle may be verified experimentally using a chemical medium like the Belouzov-Zhabotinsky reagent in the excitable regime.

Original language | English |
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Pages (from-to) | 2785-2799 |

Number of pages | 14 |

Journal | Proceedings A: Mathematical, Physical and Engineering Sciences |

Volume | 452 |

Issue number | 1955 |

Publication status | Published - 1996 |

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## Cite this

Mulholland, A. J., Gomatam, J., & McQuillan, P. (1996). Diffraction of spherical waves by a toroidal obstacle: eikonal approach to excitable reaction-diffusion systems.

*Proceedings A: Mathematical, Physical and Engineering Sciences*,*452*(1955), 2785-2799.