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

Michael Stich; Alexander S. Mikhailov

doi:10.1016/j.physd.2006.01.011

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

Michael Stich^*
, Alexander S. Mikhailov

^*Corresponding author for this work

College of Engineering and Physical Sciences

Instituto Nacional de Técnica Aeroespacial
Fritz-Haber-Institut der Max-Planck-Gesellschaft

Research output: Contribution to journal › Article › peer-review

36 Citations (Scopus)

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 language	English
Pages (from-to)	38-45
Number of pages	8
Journal	Physica D
Volume	215
Issue number	1
DOIs	https://doi.org/10.1016/j.physd.2006.01.011
Publication status	Published - 1 Mar 2006

Keywords

Pattern formation
Reaction-diffusion systems
Target patterns

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10.1016/j.physd.2006.01.011

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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.",

keywords = "Pattern formation, Reaction-diffusion systems, Target patterns",

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year = "2006",

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AU - Stich, Michael

AU - Mikhailov, Alexander S.

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N2 - 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.

AB - 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.

KW - Pattern formation

KW - Reaction-diffusion systems

KW - Target patterns

UR - https://www.scopus.com/pages/publications/33644919392

UR - https://www.sciencedirect.com/science/article/pii/S0167278906000236?via%3Dihub

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DO - 10.1016/j.physd.2006.01.011

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VL - 215

SP - 38

EP - 45

JO - Physica D

JF - Physica D

IS - 1

ER -

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

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Keywords

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