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Modulated two-dimensional patterns in reaction–diffusion systems

Published online by Cambridge University Press:  01 April 1999

R. KUSKE  and
P. MILEWSKI
R. KUSKE
Affiliation:
School of Mathematics, University of Minnesota, Minneapolis, MN, USA (email: [email protected])
P. MILEWSKI
Affiliation:
Department of Mathematics, University of Wisconsin, Madison, WI, USA (email: [email protected])
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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.

Type
Research Article
Information
European Journal of Applied Mathematics , Volume 10 , Issue 2 , April 1999 , pp. 157 - 184
Copyright
1999 Cambridge University Press

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