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Additive global noise delays Turing bifurcations

Axel Hutt 1 Andre Longtin Lutz Schimansky-Geier 
1 CORTEX - Neuromimetic intelligence
INRIA Lorraine, LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications
Abstract : We apply a stochastic center manifold method to the calculation of noise-induced phase transitions in the stochastic Swift-Hohenberg equation. This analysis is applied to the reduced mode equations that result from Fourier decomposition of the field variable and of the temporal noise. The method shows a pitchfork bifurcation at lower perturbation order, but reveals a novel additive-noise-induced postponement of the Turing bifurcation at higher order. Good agreement is found between the theory and the numerics for both the reduced and the full system. The results are generalizable to a broad class of nonlinear spatial systems.
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Axel Hutt, Andre Longtin, Lutz Schimansky-Geier. Additive global noise delays Turing bifurcations. Physical Review Letters, 2007, 98 (23), pp.230601-1 - 230601-4. ⟨10.1103/PhysRevLett.98.230601⟩. ⟨inria-00401534⟩



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