Weak-noise limit of Fokker-Planck models and nondifferentiable potentials for dissipative dynamical systems

1985 ◽  
Vol 31 (2) ◽  
pp. 1109-1122 ◽  
Author(s):  
R. Graham ◽  
T. Tél
Keyword(s):  
Dynamical Systems ◽  
Weak Noise ◽  
Noise Limit ◽  
Dissipative Dynamical Systems ◽  
Fokker Planck

On the weak-noise limit of Fokker-Planck models

1984 ◽  
Vol 35 (5-6) ◽  
pp. 729-748 ◽  
Author(s):  
R. Graham ◽  
T. T�l
Keyword(s):  
Weak Noise ◽  
Noise Limit ◽  
Fokker Planck

scholarly journals On the weak-noise limit of Fokker-Planck models

1984 ◽  
Vol 37 (5-6) ◽  
pp. 709-709 ◽  
Author(s):  
R. Graham ◽  
T. T�l
Keyword(s):  
Weak Noise ◽  
Noise Limit ◽  
Fokker Planck

Optimal Paths, Caustics, and Boundary Layer Approximations in Stochastically Perturbed Dynamical Systems

1995 ◽  
Author(s):  
Robert S. Maier ◽  
Daniel L. Stein
Keyword(s):  
Dynamical Systems ◽  
Optimal Path ◽  
Asymptotic Properties ◽  
Escape Time ◽  
Two Dimensional ◽  
Critical Systems ◽  
Weak Noise ◽  
Optimal Paths ◽  
Noise Limit ◽  
The Mean

Abstract We study the asymptotic properties of overdamped dynamical systems with one or more point attractors, when they are perturbed by weak noise. In the weak-noise limit, fluctuations to the vicinity of any specified non-attractor point will increasingly tend to follow a well-defined optimal path. We compute precise asymptotics for the frequency of such fluctuations, by integrating a matrix Riccati equation along the optimal path. We also consider noise-induced transitions between domains of attraction, in two-dimensional double well systems. The optimal paths in such systems may focus, creating a caustic. We examine ‘critical’ systems in which a caustic is beginning to form, and show that due to criticality, the mean escape time from one well to the other grows in the weak-noise limit in a non-exponential way. The analysis relies on a Maslov-WKB approximation to the solution of the Smoluchowski equation.

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