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 language | English |
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Pages (from-to) | 157-184 |
Number of pages | 28 |
Journal | European Journal of Applied Mathematics |
Volume | 10 |
Issue number | 2 |
DOIs | |
Publication status | Published - 1 Apr 1999 |
ASJC Scopus subject areas
- Applied Mathematics