Target patterns in two-dimensional heterogeneous oscillatory reaction-diffusion systems

Michael Stich*, Alexander S. Mikhailov

*Corresponding author for this work

Research output: Contribution to journalArticle

Abstract

Properties of target patterns created by pacemakers, representing local regions with the modified oscillation frequency, are studied for two-dimensional oscillatory reaction-diffusion systems described by the complex Ginzburg-Landau equation. An approximate analytical solution, based on the phase dynamics approximation, is constructed for a circular core and compared with numerical results for circular and square cores. The dependence of the wavenumber and frequency of generated waves on the size and frequency shift of the pacemaker is discussed. Instabilities of target patterns, involving repeated creations of ring-shaped amplitude defects, are further considered.

Original languageEnglish
Pages (from-to)38-45
Number of pages8
JournalPhysica D
Volume215
Issue number1
DOIs
Publication statusPublished - 1 Mar 2006

Fingerprint

Pacemakers
Reaction-diffusion System
Target
Landau-Ginzburg equations
frequency shift
Complex Ginzburg-Landau Equation
Defects
oscillations
rings
shift
defects
Analytical Solution
approximation
Oscillation
Ring
Numerical Results
Approximation

Keywords

  • Pattern formation
  • Reaction-diffusion systems
  • Target patterns

Cite this

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abstract = "Properties of target patterns created by pacemakers, representing local regions with the modified oscillation frequency, are studied for two-dimensional oscillatory reaction-diffusion systems described by the complex Ginzburg-Landau equation. An approximate analytical solution, based on the phase dynamics approximation, is constructed for a circular core and compared with numerical results for circular and square cores. The dependence of the wavenumber and frequency of generated waves on the size and frequency shift of the pacemaker is discussed. Instabilities of target patterns, involving repeated creations of ring-shaped amplitude defects, are further considered.",
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Target patterns in two-dimensional heterogeneous oscillatory reaction-diffusion systems. / Stich, Michael; Mikhailov, Alexander S.

In: Physica D, Vol. 215, No. 1, 01.03.2006, p. 38-45.

Research output: Contribution to journalArticle

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AU - Mikhailov, Alexander S.

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