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A self-organizing joint system classical oscillator + random environment isconsidered within the framework of a complex probabilistic process thatsatisfies a Langevin-type stochastic differential equation. Various types ofrandomness generated by the environment are considered. In the limit ofstatistical equilibrium (SEq), second-order partial differential equations(PDE) are derived that describe the distribution of classical environmentalfields. The mathematical expectation of the oscillator trajectory isconstructed in the form of a functional-integral representation, which, in theSEq limit, is compactified into a two-dimensional integral representation withan integrand - the solution of the second-order complex PDE. It is proved thatthe complex PDE in the general case is reduced to two independent PDEs of thesecond-order with spatially deviating arguments. The geometric and topologicalfeatures of the two-dimensional subspace on which these equations arise arestudied in detail. An algorithm for parallel modeling of the problem has beendeveloped.

Theoretical and Numerical Study of Self-Organizing Processes In a Closed System Classical Oscillator + Random Environment