The stability of spiral waves

Faridon Amdjadi, Robert Wallace

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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 languageEnglish
Title of host publicationProceedings of the International Conference on Numerical Analysis and Applied Mathematics 2009
PublisherAmerican Institute of Physics
ISBN (Print)9780735407053
DOIs
Publication statusPublished - 2009

Fingerprint

Spiral Wave
Tracing
Numerical Procedure
Reaction-diffusion System
Reaction-diffusion Equations
Rotating
Path
Dependent
Operator

Keywords

  • spiral waves
  • algorithm

Cite this

Amdjadi, F., & Wallace, R. (2009). The stability of spiral waves. In Proceedings of the International Conference on Numerical Analysis and Applied Mathematics 2009 American Institute of Physics. https://doi.org/10.1063/1.3241648
Amdjadi, Faridon ; Wallace, Robert. / The stability of spiral waves. Proceedings of the International Conference on Numerical Analysis and Applied Mathematics 2009. American Institute of Physics, 2009.
@inproceedings{ce3b188da932458bbca8f4dc699c0cf9,
title = "The stability of spiral waves",
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.",
keywords = "spiral waves, algorithm",
author = "Faridon Amdjadi and Robert Wallace",
note = "<p>Paper presented at the International Conference on Numerical Analysis and Applied Mathematics, Crete, Greece, 18-22 September 2009. Proceedings ISBN: 9780735407053.</p>",
year = "2009",
doi = "10.1063/1.3241648",
language = "English",
isbn = "9780735407053",
booktitle = "Proceedings of the International Conference on Numerical Analysis and Applied Mathematics 2009",
publisher = "American Institute of Physics",
address = "United States",

}

Amdjadi, F & Wallace, R 2009, The stability of spiral waves. in 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.

Proceedings of the International Conference on Numerical Analysis and Applied Mathematics 2009. American Institute of Physics, 2009.

Research output: Chapter in Book/Report/Conference proceedingConference 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 -

Amdjadi F, Wallace R. The stability of spiral waves. In Proceedings of the International Conference on Numerical Analysis and Applied Mathematics 2009. American Institute of Physics. 2009 https://doi.org/10.1063/1.3241648