### Abstract

A class of non-equilibrium media described by equations close to gradient one is considered. For the analysis of the field structure dynamics in such media an asymptotic method is proposed where the generating solution is that of the gradient system. The analysis is based on the generalised Ginzburg-Landau equation. For in =O this equation can be written as delta a/ delta t=- delta F(a)/ delta a* where F is the Lyapunov functional: F=(f( mod a mod ^{2})+ mod a mod ^{2}) dx dy and solutions are possible in the form of static spiral waves centred on the point (x, y). When O( in <<1 a solution is sought in the form of an asymptotic series with the first term having the form of a spiral wave, but the parameters x, y and phase will be slow functions of time. Using this method the interaction of a pair of spiral waves in media with hard and soft excitation is investigated and the stochastic drift of a spiral wave in a periodically inhomogenous field is predicted.

Original language | English (US) |
---|---|

Article number | 014 |

Pages (from-to) | 299-318 |

Number of pages | 20 |

Journal | Journal of Physics A: Mathematical and General |

Volume | 23 |

Issue number | 3 |

DOIs | |

State | Published - Dec 1 1990 |

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### All Science Journal Classification (ASJC) codes

- Statistical and Nonlinear Physics
- Mathematical Physics
- Physics and Astronomy(all)

### Cite this

*Journal of Physics A: Mathematical and General*,

*23*(3), 299-318. [014]. https://doi.org/10.1088/0305-4470/23/3/014

}

*Journal of Physics A: Mathematical and General*, vol. 23, no. 3, 014, pp. 299-318. https://doi.org/10.1088/0305-4470/23/3/014

**Dynamics of spiral waves in non-equilibrium media.** / Aronson, Igor; Rabinovich, M. I.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Dynamics of spiral waves in non-equilibrium media

AU - Aronson, Igor

AU - Rabinovich, M. I.

PY - 1990/12/1

Y1 - 1990/12/1

N2 - A class of non-equilibrium media described by equations close to gradient one is considered. For the analysis of the field structure dynamics in such media an asymptotic method is proposed where the generating solution is that of the gradient system. The analysis is based on the generalised Ginzburg-Landau equation. For in =O this equation can be written as delta a/ delta t=- delta F(a)/ delta a* where F is the Lyapunov functional: F=(f( mod a mod 2)+ mod a mod 2) dx dy and solutions are possible in the form of static spiral waves centred on the point (x, y). When O( in <<1 a solution is sought in the form of an asymptotic series with the first term having the form of a spiral wave, but the parameters x, y and phase will be slow functions of time. Using this method the interaction of a pair of spiral waves in media with hard and soft excitation is investigated and the stochastic drift of a spiral wave in a periodically inhomogenous field is predicted.

AB - A class of non-equilibrium media described by equations close to gradient one is considered. For the analysis of the field structure dynamics in such media an asymptotic method is proposed where the generating solution is that of the gradient system. The analysis is based on the generalised Ginzburg-Landau equation. For in =O this equation can be written as delta a/ delta t=- delta F(a)/ delta a* where F is the Lyapunov functional: F=(f( mod a mod 2)+ mod a mod 2) dx dy and solutions are possible in the form of static spiral waves centred on the point (x, y). When O( in <<1 a solution is sought in the form of an asymptotic series with the first term having the form of a spiral wave, but the parameters x, y and phase will be slow functions of time. Using this method the interaction of a pair of spiral waves in media with hard and soft excitation is investigated and the stochastic drift of a spiral wave in a periodically inhomogenous field is predicted.

UR - http://www.scopus.com/inward/record.url?scp=0011303716&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0011303716&partnerID=8YFLogxK

U2 - 10.1088/0305-4470/23/3/014

DO - 10.1088/0305-4470/23/3/014

M3 - Article

AN - SCOPUS:0011303716

VL - 23

SP - 299

EP - 318

JO - Journal of Physics A: Mathematical and Theoretical

JF - Journal of Physics A: Mathematical and Theoretical

SN - 1751-8113

IS - 3

M1 - 014

ER -