Stochastically forced Hopf bifurcation: Approximate Fokker-Planck equation in the limit of short correlation times
- 1 May 1988
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review A
- Vol. 37 (9) , 3630-3633
- https://doi.org/10.1103/physreva.37.3630
Abstract
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)].Keywords
This publication has 31 references indexed in Scilit:
- Unitary point of view on the puzzling problem of nonlinear systems driven by colored noisePhysical Review A, 1987
- Dynamical systems: A unified colored-noise approximationPhysical Review A, 1987
- Bistability driven by Gaussian colored noise: First-passage timesPhysical Review A, 1987
- A new method of analysis of the effect of weak colored noise in nonlinear dynamical systemsJournal of Statistical Physics, 1987
- Laser-noise analysis by first-passage-time techniquesPhysical Review A, 1986
- Mean first-passage time of continuous non-Markovian processes driven by colored noisePhysical Review A, 1986
- Bistability driven by colored noise: Theory and experimentPhysical Review A, 1985
- Finite correlation time effects in nonequilibrium phase transitionsPhysica A: Statistical Mechanics and its Applications, 1983
- Analytical and numerical studies of multiplicative noisePhysical Review A, 1982
- White and coloured external noise and transition phenomena in nonlinear systemsZeitschrift für Physik B Condensed Matter, 1978