scholarly journals On a class of exact solutions to the Fokker–Planck equations

1982 ◽  
Vol 23 (6) ◽  
pp. 1155-1158 ◽  
Author(s):  
L. Garrido ◽  
J. Masoliver
Keyword(s):  
Exact Solutions ◽  
Fokker Planck Equations ◽  
Fokker Planck

Random Vibrations in Discrete Nonlinear Dynamic Systems

1968 ◽  
Vol 10 (2) ◽  
pp. 168-174 ◽  
Author(s):  
R. G. Bhandari ◽  
R. E. Sherrer
Keyword(s):  
Exact Solutions ◽  
Density Function ◽  
Gaussian White Noise ◽  
Hermite Polynomials ◽  
Planck Equation ◽  
Degree Of Freedom ◽  
Multiple Series ◽  
Special Cases ◽  
Fokker Planck Equations ◽  
Fokker Planck

A one-degree-of-freedom system and a two-degree-of-freedom system containing Dis-placement and velocity dependent nonlinearities subjected to stationary gaussian white noise excitation have been studied by the method of the Fokker-Planck equation. Non-linearities have been represented by suitable polynomials. The Fokker-Planck equations governing the stationary probability density function for these systems have been solved by representing the density function by a multiple series of Hermite polynomials. The constants in the series expansion were determined by Galerkin's method. Analysis is developed for the system containing nonlinearities described by suitable polynomials in velocity and displacement dependent forces. Comparisons were made between series and exact solutions for those special cases for which exact solutions are known.

Exact solutions of Fokker-Planck equations associated to quantum wave functions

1998 ◽  
Vol 245 (1-2) ◽  
pp. 1-10 ◽  
Author(s):  
Nicola Cufaro Petroni ◽  
Salvatore De Martino ◽  
Silvio De Siena
Keyword(s):  
Exact Solutions ◽  
Wave Functions ◽  
Quantum Wave ◽  
Fokker Planck Equations ◽  
Fokker Planck

scholarly journals Dynamical Study of Fokker-Planck Equations by Using Optimal Homotopy Asymptotic Method

Mathematics ◽  
2019 ◽  
Vol 7 (3) ◽  
pp. 264 ◽  
Author(s):  
H. Younas ◽  
Muhammad Mustahsan ◽  
Tareq Manzoor ◽  
Nadeem Salamat ◽  
S. Iqbal
Keyword(s):  
Convergence Rate ◽  
Exact Solutions ◽  
Fractional Order ◽  
Asymptotic Method ◽  
Dynamical Study ◽  
Optimal Homotopy Asymptotic Method ◽  
Relative Errors ◽  
Fokker Planck Equations ◽  
Fokker Planck

In this article, Optimal Homotopy Asymptotic Method (OHAM) is used to approximate results of time-fractional order Fokker-Planck equations. In this work, 3rd order results obtained through OHAM are compared with the exact solutions. It was observed that results from OHAM have better convergence rate for time-fractional order Fokker-Planck equations. The solutions are plotted and the relative errors are tabulated.

scholarly journals Fokker–Planck representations of non-Markov Langevin equations: application to delayed systems

2019 ◽  
Vol 377 (2153) ◽  
pp. 20180131 ◽  
Author(s):  
Luca Giuggioli ◽  
Zohar Neu
Keyword(s):  
Langevin Equation ◽  
Complex Dynamics ◽  
Probability Distributions ◽  
Delay Systems ◽  
Langevin Equations ◽  
Delayed Systems ◽  
Temporal Features ◽  
Fokker Planck Equations ◽  
Random Fluctuations ◽  
Fokker Planck

Noise and time delays, or history-dependent processes, play an integral part in many natural and man-made systems. The resulting interplay between random fluctuations and time non-locality are essential features of the emerging complex dynamics in non-Markov systems. While stochastic differential equations in the form of Langevin equations with additive noise for such systems exist, the corresponding probabilistic formalism is yet to be developed. Here we introduce such a framework via an infinite hierarchy of coupled Fokker–Planck equations for the n -time probability distribution. When the non-Markov Langevin equation is linear, we show how the hierarchy can be truncated at n  = 2 by converting the time non-local Langevin equation to a time-local one with additive coloured noise. We compare the resulting Fokker–Planck equations to an earlier version, solve them analytically and analyse the temporal features of the probability distributions that would allow to distinguish between Markov and non-Markov features. This article is part of the theme issue ‘Nonlinear dynamics of delay systems’.

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