Solving phase-noise Fokker-Planck equations using the motion-group Fourier transform

2006 ◽  
Vol 54 (5) ◽  
pp. 868-877 ◽  
Author(s):  
Yunfeng Wang ◽  
Yu Zhou ◽  
D.K. Maslen ◽  
G.S. Chirikjian
Keyword(s):  
Fourier Transform ◽  
Phase Noise ◽  
Motion Group ◽  
Group Fourier Transform ◽  
Fokker Planck Equations ◽  
Fokker Planck

The Stochastic Resonance of Noise Frequency Modulation Signal Using Motion-Group Fourier Transform

2015 ◽  
Vol 713-715 ◽  
pp. 1452-1455
Author(s):  
Jing Bo He ◽  
Sheng Liang Hu
Keyword(s):  
Signal Processing ◽  
Fourier Transform ◽  
Stochastic Resonance ◽  
Frequency Modulation ◽  
Planck Equation ◽  
Motion Group ◽  
Noise Frequency ◽  
Modulation Signal ◽  
Group Fourier Transform ◽  
Linear Differential

In this paper stochastic resonance was studied in radar driven by noise frequency modulation signal. According to the intrinsic relations between the stochastic differential and the radar jamming signal processing, the stochastic calculus was used in the radar jamming signal processing in this paper. The noise frequency modulation signal was particularly analyzed. The Fokker-Planck equation of noise frequency modulation was presented and the Motion-Group Fourier Transform was used by converting the partial differential equation into the variable coefficient homogenous linear differential equations. Then the solutions were given.

scholarly journals An analysis of phase noise and Fokker–Planck equations

2007 ◽  
Vol 234 (2) ◽  
pp. 391-411 ◽  
Author(s):  
Shui-Nee Chow ◽  
Hao-Min Zhou
Keyword(s):  
Phase Noise ◽  
Fokker Planck Equations ◽  
Fokker Planck

scholarly journals AnLp-Lq-Version of Morgan's Theorem for then-Dimensional Euclidean Motion Group

2007 ◽  
Vol 2007 ◽  
pp. 1-9
Author(s):  
Sihem Ayadi ◽  
Kamel Mokni
Keyword(s):  
Fourier Transform ◽  
Motion Group ◽  
Euclidean Motion Group ◽  
Euclidean Motion ◽  
Group Fourier Transform

We establish anLp-Lq-version of Morgan's theorem for the group Fourier transform on then-dimensional Euclidean motion groupM(n).

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’.

Modified Fokker-Planck equations

1978 ◽  
Vol 36 (1) ◽  
pp. 65-78 ◽  
Author(s):  
Glenn T. Evans
Keyword(s):  
Fokker Planck Equations ◽  
Fokker Planck
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