scholarly journals Analytical approximation to the multidimensional Fokker–Planck equation with steady state

2019 ◽  
Vol 52 (8) ◽  
pp. 085002 ◽  
Author(s):  
R J Martin ◽  
R V Craster ◽  
A Pannier ◽  
M J Kearney
Keyword(s):  
Steady State ◽  
Planck Equation ◽  
Analytical Approximation ◽  
Fokker Planck Equation ◽  
Fokker Planck

Richards Growth Model Driven by Multiplicative and Additive Colored Noises: Steady-State Analysis

2020 ◽  
Vol 19 (04) ◽  
pp. 2050032
Author(s):  
Chaoqun Xu ◽  
Sanling Yuan
Keyword(s):  
Steady State ◽  
Stochastic Model ◽  
Growth Model ◽  
Planck Equation ◽  
Steady State Analysis ◽  
Model Driven ◽  
Fokker Planck Equation ◽  
Richards Growth Model ◽  
Fokker Planck ◽  
State Analysis

We consider a Richards growth model (modified logistic model) driven by correlated multiplicative and additive colored noises, and investigate the effects of noises on the eventual distribution of population size with the help of steady-state analysis. An approximative Fokker–Planck equation is first derived for the stochastic model. By performing detailed theoretical analysis and numerical simulation for the steady-state solution of the Fokker–Planck equation, i.e., stationary probability distribution (SPD) of the stochastic model, we find that the correlated noises have complex effects on the statistical property of the stochastic model. Specifically, the phenomenological bifurcation may be caused by the noises. The position of extrema of the SPD depends on the model parameter and the characters of noises in different ways.

scholarly journals THE WIGNER–FOKKER–PLANCK EQUATION: STATIONARY STATES AND LARGE TIME BEHAVIOR

2012 ◽  
Vol 22 (11) ◽  
pp. 1250034 ◽  
Author(s):  
ANTON ARNOLD ◽  
IRENE M. GAMBA ◽  
MARIA PIA GUALDANI ◽  
STÉPHANE MISCHLER ◽  
CLEMENT MOUHOT ◽  
...  
Keyword(s):  
Steady State ◽  
Large Time ◽  
Planck Equation ◽  
Large Time Behavior ◽  
Positive Density ◽  
Time Behavior ◽  
Spectral Gaps ◽  
Harmonic Oscillator Potential ◽  
Fokker Planck Equation ◽  
Fokker Planck

We consider the linear Wigner–Fokker–Planck equation subject to confining potentials which are smooth perturbations of the harmonic oscillator potential. For a certain class of perturbations we prove that the equation admits a unique stationary solution in a weighted Sobolev space. A key ingredient of the proof is a new result on the existence of spectral gaps for Fokker–Planck type operators in certain weighted L2-spaces. In addition we show that the steady state corresponds to a positive density matrix operator with unit trace and that the solutions of the time-dependent problem converge towards the steady state with an exponential rate.

Sign in / Sign up

Export Citation Format

Share Document