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1.
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 Hamilton-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. 相似文献
2.
K. Mallick P. Marcq 《The European Physical Journal B - Condensed Matter and Complex Systems》2003,31(4):553-561
We study analytically and numerically the problem of a nonlinear mechanical oscillator with additive noise in the absence
of damping. We show that the amplitude, the velocity and the energy of the oscillator grow algebraically with time. For Gaussian
white noise, an analytical expression for the probability distribution function of the energy is obtained in the long-time
limit. In the case of colored, Ornstein-Uhlenbeck noise, a self-consistent calculation leads to (different) anomalous diffusion
exponents. Dimensional analysis yields the qualitative behavior of the prefactors (generalized diffusion constants) as a function
of the correlation time.
Received 10 October 2002 Published online 6 March 2003
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ID="a"e-mail: mallick@spht.saclay.cea.fr 相似文献
3.
J.M. Sancho A. Sánchez 《The European Physical Journal B - Condensed Matter and Complex Systems》2000,16(1):127-131
We study the dynamics of fronts when both inertial effects and external fluctuations are taken into account. Stochastic fluctuations
are introduced as multiplicative white noise arising from a control parameter of the system. Contrary to the non-inertial
(overdamped) case, we find that important features of the system, such as the velocity selection picture, are not modified
by the noise. We then compute the overdamped limit of the underdamped dynamics in a more careful way, finding that it does
not exhibit any effect of noise either. Our result poses the question as to whether or not external noise sources can be measured
in physical systems of this kind.
Received 2 July 1999 and Received in final form 25 November 1999 相似文献