Theory of interaction and bound states of spiral waves in oscillatory media

Igor Aronson, Lorenz Kramer, Andreas Weber

Research output: Contribution to journalArticle

77 Citations (Scopus)

Abstract

We present an alternative method for the calculation of the interaction between spirals in oscillatory media. This method is based on a rigorous evaluation of the perturbation of an isolated spiral resulting from neighboring spirals in a linear approximation. For the complex Ginzburg-Landau equation, the existence of bound states is identified with the parameter range where the perturbations behave in an oscillatory manner. The results for the equilibrium distance for two spirals in the bound state and also the dependence of the velocity of the spiral on the distance are in good agreement with numerical simulations. In the equally charged case, we find multiple bound states which may be interpreted as multiply armed spirals. Outside the oscillatory range, well-separated spirals appear to repel each other regardless of topological charge.

Original languageEnglish (US)
Pages (from-to)3231-3241
Number of pages11
JournalPhysical Review E
Volume47
Issue number5
DOIs
StatePublished - Jan 1 1993

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Spiral Wave
Bound States
Interaction
interactions
Perturbation
perturbation
Complex Ginzburg-Landau Equation
Landau-Ginzburg equations
Linear Approximation
Range of data
Multiplication
Charge
Numerical Simulation
evaluation
Alternatives
Evaluation
approximation

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Condensed Matter Physics
  • Physics and Astronomy(all)

Cite this

Aronson, Igor ; Kramer, Lorenz ; Weber, Andreas. / Theory of interaction and bound states of spiral waves in oscillatory media. In: Physical Review E. 1993 ; Vol. 47, No. 5. pp. 3231-3241.
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Theory of interaction and bound states of spiral waves in oscillatory media. / Aronson, Igor; Kramer, Lorenz; Weber, Andreas.

In: Physical Review E, Vol. 47, No. 5, 01.01.1993, p. 3231-3241.

Research output: Contribution to journalArticle

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