Abstract
We prove, using normal form techniques in a codimension one bifurcation, that the conditional probability of the fast variable conditioned by the slow variables is a Gaussian distribution centered in the center manifold.
This is a preview of subscription content, log in via an institution to check access.
References
E. Knobloch and K. A. Wiesenfeld,J. Stat. Phys. 33:611 (1983).
F. Baras, P. Coullet, and E. Tirapegui,J. Stat. Phys. 45:745 (1986).
C. Elphick, E. Tirapegui, M. E. Brachet, P. Coullet, and G. Tooss, A simple global characterization for normal forms of singular vector fields, Preprint, Université de Nice NTH 86/6; to be published inPhysica D.
N. G. van Kampen,Stochastic Processes in Physics and Chemistry (North-Holland, Amsterdam, 1981), Chapter VIII.6.
C. van den Broeck, M. Malek-Mansour, and F. Baras,J. Stat. Phys. 28:557 (1982).
J. M. Sancho and M. San Miguel,Z. Phys. B 36:357 (1980).
P. Coullet, C. Elphick, and E. Tirapegui,Phys. Lett. 111A:277 (1985).
V. Arnold,Chapitres Supplémentaires de la Théorie des Equations Différentielles Ordinaires (MIR, Moscow, 1980).
F. Langouche, D. Roekaerts, and E. Tirapegui,Functional Integration and Semiclassical Expansions (Reidel, 1982), Chapter VII.6.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Elphick, C., Jeanneret, M. & Tirapegui, E. Comment on bifurcations in fluctuating systems. J Stat Phys 48, 925–933 (1987). https://doi.org/10.1007/BF01019703
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01019703