The stability of spiral waves

Faridon Amdjadi; Robert Wallace

doi:10.1063/1.3241648

The stability of spiral waves

Faridon Amdjadi, Robert Wallace

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

Abstract

Itis well known that the spiral wave solution of thereaction-diffusion equations is in the form of two qualitatively differentclasses of waves: rigidly rotating spirals or meandering spiral waves.The main objective of this paper is to study thestability of these waves. We develop an algorithm to dealwith an operator dependent linearized system and to show thatthese waves are stable. This algorithm could be easily implemented.We also introduce a new approach for studying the dynamicschange in the reaction diffusion system that obviates the needfor tracing the path of spiral tip. Unlike tracing outthe spiral tip which requires the intensive numerical procedures, ourapproach 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	https://doi.org/10.1063/1.3241648
Publication status	Published - 2009
Event	International Conference on Numerical Analysis and Applied Mathematics 2009 - Crete, Greece Duration: 18 Sept 2009 → 22 Sept 2009

Conference

Conference	International Conference on Numerical Analysis and Applied Mathematics 2009
Abbreviated title	ICNAAM
Country/Territory	Greece
City	Crete
Period	18/09/09 → 22/09/09

Keywords

spiral waves
algorithm

Documents and Links

10.1063/1.3241648

Cite this

@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>; International Conference on Numerical Analysis and Applied Mathematics 2009, ICNAAM ; Conference date: 18-09-2009 Through 22-09-2009",

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",

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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

T2 - International Conference on Numerical Analysis and Applied Mathematics 2009

Y2 - 18 September 2009 through 22 September 2009

ER -

The stability of spiral waves

Abstract

Conference

Keywords

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Cite this