### Abstract

It^{ }is well known that the spiral wave solution of the^{ }reaction-diffusion equations is in the form of two qualitatively different^{ }classes of waves: rigidly rotating spirals or meandering spiral waves.^{ }The main objective of this paper is to study the^{ }stability of these waves. We develop an algorithm to deal^{ }with an operator dependent linearized system and to show that^{ }these waves are stable. This algorithm could be easily implemented.^{ }We also introduce a new approach for studying the dynamics^{ }change in the reaction diffusion system that obviates the need^{ }for tracing the path of spiral tip. Unlike tracing out^{ }the spiral tip which requires the intensive numerical procedures, our^{ }approach is easily implemented.

Original language | English |
---|---|

Title of host publication | Proceedings of the International Conference on Numerical Analysis and Applied Mathematics 2009 |

Publisher | American Institute of Physics |

ISBN (Print) | 9780735407053 |

DOIs | |

Publication status | Published - 2009 |

### Fingerprint

### Keywords

- spiral waves
- algorithm

### Cite this

*Proceedings of the International Conference on Numerical Analysis and Applied Mathematics 2009*American Institute of Physics. https://doi.org/10.1063/1.3241648

}

*Proceedings of the International Conference on Numerical Analysis and Applied Mathematics 2009.*American Institute of Physics. https://doi.org/10.1063/1.3241648

**The stability of spiral waves.** / Amdjadi, Faridon; Wallace, Robert.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

TY - GEN

T1 - The stability of spiral waves

AU - Amdjadi, Faridon

AU - Wallace, Robert

N1 - <p>Paper presented at the International Conference on Numerical Analysis and Applied Mathematics, Crete, Greece, 18-22 September 2009. Proceedings ISBN: 9780735407053.</p>

PY - 2009

Y1 - 2009

N2 - It is well known that the spiral wave solution of the reaction-diffusion equations is in the form of two qualitatively different classes of waves: rigidly rotating spirals or meandering spiral waves. The main objective of this paper is to study the stability of these waves. We develop an algorithm to deal with an operator dependent linearized system and to show that these waves are stable. This algorithm could be easily implemented. We also introduce a new approach for studying the dynamics change in the reaction diffusion system that obviates the need for tracing the path of spiral tip. Unlike tracing out the spiral tip which requires the intensive numerical procedures, our approach is easily implemented.

AB - It is well known that the spiral wave solution of the reaction-diffusion equations is in the form of two qualitatively different classes of waves: rigidly rotating spirals or meandering spiral waves. The main objective of this paper is to study the stability of these waves. We develop an algorithm to deal with an operator dependent linearized system and to show that these waves are stable. This algorithm could be easily implemented. We also introduce a new approach for studying the dynamics change in the reaction diffusion system that obviates the need for tracing the path of spiral tip. Unlike tracing out the spiral tip which requires the intensive numerical procedures, our approach is easily implemented.

KW - spiral waves

KW - algorithm

U2 - 10.1063/1.3241648

DO - 10.1063/1.3241648

M3 - Conference contribution

SN - 9780735407053

BT - Proceedings of the International Conference on Numerical Analysis and Applied Mathematics 2009

PB - American Institute of Physics

ER -