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Stochastically forced Hopf bifurcation: Approximate Fokker-Planck equation in the limit of short correlation times

par Altares Menendez, Valentin ;Nicolis, Grégoire
Référence Physical review. A, General physics, 37, 9, page (3630-3633)
Publication Publié, 1988

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Résumé :

We derive an approximate Fokker-Planck equation up to first order in the correlation time for a stochastically forced Hopf bifurcation. The general results are illustrated on the Brusselator model. In the range of validity of our approximation, it is shown that the noise always postpones the bifurcation point (appearance of new extrema of the probability distribution). This shift is a decreasing function of the correlation time. Qualitative agreement is found with recent experimental observations [L. Fronzoni, R. Mannella, P. Mc Clintock, and F. Moss, Phys. Rev. A 36, 834 (1987)]. © 1988 The American Physical Society.