Stationary Solution Of Fokker-Planck Equation Research Articles

Numerical Study on Fokker-Planck Equation of Bistable System Driven by Colored Noise

A finite difference method is used to solve a Fokker-Planck equation of bistable system with Landau potential. The detailed dynamical relaxation process in the case of large correlation time is manifested via the phenomena including the saddle point appearance, the hole formation and distortion. The method is used to obtain the stationary solutions of Fokker-Planck equation of bistable system driven by rather weak noise.

Exact Stationary Solution of Fokker-Planck Equation and Generalized Potential for Non-Equilibrium Systems Without Detailed Balance

An exact analogy is approached between systems in thermal equilibrium and those far from equilibrium which can be the cases without detailed balance. The analogy is based on the requirement that a given drift in the Fokker-Planck equation can be decomposed into two parts, one of which is divergence-free and the other can be derived from a potential which is invariant along the direction of the first part. If the conditions are fulfilled the Fokker-Planck equation changes in to a standard Poisson equation. The relations of this requirement to other conditions are discussed. As a concrete example, the stationary Fokker-Planck equation for optical bistability is solved by using this method.

Stationary solution of the Fokker-Planck equation for the continuum mode laser with spatially inhomogeneous dissipation and excitation

An approximation scheme is developed in order to obtain an expression for the stationary solution of the multivariate nonlinear Fokker-Planck equation for the continuum mede laser having spatially inhomogeneous losses and inversion. This Fokker-Planck equation, being valid throughout the threshold region, has been derived in a previous paper. After diagonalizing the linear drift matrix the so-called diagonal diffusion approximation will be introduced, which permits to find the stationary probability distribution for the mode amplitudes within the quasi-plane-wave approximation.