  A self-organizing joint system classical oscillator + random environment is
considered within the framework of a complex probabilistic process that
satisfies a Langevin-type stochastic differential equation. Various types of
randomness generated by the environment are considered. In the limit of
statistical equilibrium (SEq), second-order partial differential equations
(PDE) are derived that describe the distribution of classical environmental
fields. The mathematical expectation of the oscillator trajectory is
constructed in the form of a functional-integral representation, which, in the
SEq limit, is compactified into a two-dimensional integral representation with
an integrand - the solution of the second-order complex PDE. It is proved that
the complex PDE in the general case is reduced to two independent PDEs of the
second-order with spatially deviating arguments. The geometric and topological
features of the two-dimensional subspace on which these equations arise are
studied in detail. An algorithm for parallel modeling of the problem has been
developed.
