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Title: New method of analysis of the effect of weak colored noise in nonlinear dynamical systems

Abstract

A systematic method for obtaining the asymptotic behavior of a dynamical system forced by colored noise in the limit of small intensity is developed. It is based on the search of WKB solutions to the Fokker-Planck equation for the joint probability density of the system and noise, in which the perturbation expansion is continued to the first correction beyond the Hamiltonian-Jacobi limit. The method can be applied to noise with correlation time of order unity. It is illustrated on the normal form of a pitchfork bifurcation, where it is pointed out that additive noise can induce a shift of the most probable value. This prediction is confirmed by numerical simulation of the stochastic differential equations.

Authors:
;
Publication Date:
Research Org.:
Faculte des Sciences, Universite Libre de Bruxelles, 1050 Bruxelles, Belgium
OSTI Identifier:
6686864
Resource Type:
Journal Article
Journal Name:
J. Stat. Phys.; (United States)
Additional Journal Information:
Journal Volume: 46:1
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; STOCHASTIC PROCESSES; NOISE; FOKKER-PLANCK EQUATION; NONLINEAR PROBLEMS; WKB APPROXIMATION; DIFFERENTIAL EQUATIONS; EQUATIONS; PARTIAL DIFFERENTIAL EQUATIONS; 657000* - Theoretical & Mathematical Physics

Citation Formats

Altares, V, and Nicolis, G. New method of analysis of the effect of weak colored noise in nonlinear dynamical systems. United States: N. p., 1987. Web. doi:10.1007/BF01010340.
Altares, V, & Nicolis, G. New method of analysis of the effect of weak colored noise in nonlinear dynamical systems. United States. doi:10.1007/BF01010340.
Altares, V, and Nicolis, G. Thu . "New method of analysis of the effect of weak colored noise in nonlinear dynamical systems". United States. doi:10.1007/BF01010340.
@article{osti_6686864,
title = {New method of analysis of the effect of weak colored noise in nonlinear dynamical systems},
author = {Altares, V and Nicolis, G},
abstractNote = {A systematic method for obtaining the asymptotic behavior of a dynamical system forced by colored noise in the limit of small intensity is developed. It is based on the search of WKB solutions to the Fokker-Planck equation for the joint probability density of the system and noise, in which the perturbation expansion is continued to the first correction beyond the Hamiltonian-Jacobi limit. The method can be applied to noise with correlation time of order unity. It is illustrated on the normal form of a pitchfork bifurcation, where it is pointed out that additive noise can induce a shift of the most probable value. This prediction is confirmed by numerical simulation of the stochastic differential equations.},
doi = {10.1007/BF01010340},
journal = {J. Stat. Phys.; (United States)},
number = ,
volume = 46:1,
place = {United States},
year = {1987},
month = {1}
}