Instabilities of wave trains and turing patterns in large domains

Jens D.M. Rademacher; Arnd Scheel

doi:10.1142/S0218127407018683

Instabilities of wave trains and turing patterns in large domains

Jens D.M. Rademacher, Arnd Scheel

School of Mathematics

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

29 Scopus citations

Abstract

We classify generic instabilities of wave trains in reaction-diffusion systems on the real line as the wavenumber and system parameters are varied. We find three types of robust instabilities: Hopf with nonzero modulational wavenumber, sideband and spatio-temporal period-doubling. Near a fold, the only other robust instability mechanism, we show that all wave trains are necessarily unstable. We also discuss the special cases of homogeneous oscillations and reflection symmetric, stationary Turing patterns.

Original language	English (US)
Pages (from-to)	2679-2691
Number of pages	13
Journal	International Journal of Bifurcation and Chaos
Volume	17
Issue number	8
DOIs	https://doi.org/10.1142/S0218127407018683
State	Published - Aug 2007

Bibliographical note

Funding Information:
This work was partially supported by the National Science Foundation through grant NSF DMS-0504271 (A. Scheel), and the Priority Program SPP 1095 of the DFG as well as the NDNS+ cluster of the NWO (J. Rademacher).

Keywords

Classification of instabilities
Reaction-diffusion systems
Stability
Wave trains

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AU - Scheel, Arnd

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AB - We classify generic instabilities of wave trains in reaction-diffusion systems on the real line as the wavenumber and system parameters are varied. We find three types of robust instabilities: Hopf with nonzero modulational wavenumber, sideband and spatio-temporal period-doubling. Near a fold, the only other robust instability mechanism, we show that all wave trains are necessarily unstable. We also discuss the special cases of homogeneous oscillations and reflection symmetric, stationary Turing patterns.

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KW - Stability

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Instabilities of wave trains and turing patterns in large domains

Abstract

Bibliographical note

Keywords

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