Chaotic series are widely used to describe processes in the modern world. A substantial part of them has a complex theoretical description or has not it at all. One such description is the Fokker-Planck equation. This project is dedicated to the investigation of a particular case of the Fokker-Planck equation. We consider two different problem definitions to search for the solution to this equation.

1. Variational formulation. This statement is concerned with the minimization of function-dependent integral by variating it. The such definition allows making a connection with physics. For example, one of similar tasks is finding the path, which minimizes spent energy.
2. Differential formulation, which is equivalent for the previous one. This formulation includes Boundary value problem and can be solved using Newton-Raphson method. Practically, this method consists of multiple solving Cauchy problem with Runge-Kutta method. For stepping is used inversed matrix of residual derivatives until convergence.

However, the determinant of the derivative matrix can be close to zero. This property, surprisingly, provides useful information. A singular matrix is a criterion of the bifurcation point. These points generate an extra solution in the neighborhood of the considered point. The hypothesis is that such points in chaotic time series correspond to trend change and help to forecast their behavior. The first goal is searching bifurcation points using abovementioned criteria.

Numerical methods cause inaccuracies, and for some parameter values, the iterative algorithm diverges. To avoid such cases, we implement the parameter continuation method. After starting from zero, we continue small parameter steps until the intersection with another branch.

After finding the bifurcation point, we build branches generated by additional solutions. We use the parameter-changing method to identify them. This method fixes parameter values and changes functions. The motivation for using it is an observation that function structure varies on different branches. For plotting function branches used Frobenius norm of function values' vector.