Bifurcational Analysis of Fokker-Planck Equations

The paper is dedicated to the application of an algorithm based on the generalized Kantorovich iterative method to bifurcation analysis of stationary solutions of the Fokker-Planck equation. The algorithm deals with a problem formulated as a system of nonlinear differential equations with boundary conditions. Solving the multidimensional problem involves solving sequentially one-dimensional ordinary differential equations, and one-dimensional boundary value problems are reduced to initial value problems. The main task is to identify bifurcations - points where the system transitions to qualitatively different states due to continuous changes of a parameter. The necessary criterion for a bifurcation is the singularity of the matrix of partial derivatives of residuals that arises during the solution of boundary value problems. For the identified bifurcation points, we determine the nature of solutions near the point.