Europhys. Lett, 48 (2), pp. 156-162 (1999)
Instabilities of one-dimensional cellular patterns:
Far from the secondary threshold
INLN, UMR CNRS 129, Université
de Nice Sophia Antipolis
1361 Route des Lucioles, F-06560 Valbonne, France
(received 11 September 1998; accepted in final form 12 August 1999)
PACS. 47.10 - General theory.
PACS. 05.45 - Nonlinear dynamics and nonlinear dynamical systems.
PACS. 47.20Ky - Nonlinearity (including bifurcation theory).
Using local and global symmetry arguments, we present a phenomenological model of the instabilities of one-dimensional stationary cellular pattern far from the instability threshold. Our theory differs from those of Coullet and Iooss (Phys. Rev. Lett. 64 (1990) 866), which is valid close to the instability threshold, by the introduction of a new theoretical field, taking into account the possible phase mismatch between the basic cellular pattern and the unstable spatial pattern associated with the secondary bifurcation. Preliminary numerical simulations suggest that this new theoretical framework might be successfully used to describe some previously unexplained experimental observations.
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