Modulated two-dimensional patterns in reaction-diffusion systems

R. Kuske, P. Milewski

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Abstract

New modulation equations for hexagonal patterns in reaction-diffusion systems are derived for parameter régimes corresponding to the onset of patterns. These systems include additional nonlinearities which are not present in Rayleigh-Bénard convection or Swift-Hohenberg type models. The dynamics of hexagonal and roll patterns are studied using a combination of analytical and computational approaches which exploit the hexagonal structure of the modulation equations. The investigation demonstrates instabilities and new phenomena not found in other systems, and is applied to patterns of flame fronts in a certain model of burner stabilized flames.

Original languageEnglish (US)
Pages (from-to)157-184
Number of pages28
JournalEuropean Journal of Applied Mathematics
Volume10
Issue number2
DOIs
StatePublished - 1999

All Science Journal Classification (ASJC) codes

  • Applied Mathematics

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