Additive global noise delays Turing bifurcations

Axel Hutt (1) , Andre Longtin (2) , Lutz Schimansky-Geier (3)

1 MIMESIS - Computational Anatomy and Simulation for Medicine
2 Department of Physics [Ottawa]
3 HU Berlin - Humboldt-Universität zu Berlin = Humboldt University of Berlin = Université Humboldt de Berlin

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.

Domaines: Modélisation et simulation

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⟩