ABSTRACT
When analyzing phenomena and processes of the real world either experimentally or theoretically, one cannot represent them in a “pure” form. In other words, no matter how accurately one takes into account the forces initiating the phenomenon in question, arbitrarily small perturbations are always left unexplained. The desire to describe this situation adequately generates a need to expand the techniques applicable to the mathematical analysis of the phenomenon in question. Within the framework of the description of phenomena by using ordinary differential equations (finite-dimensional ones or equations in Banach spaces), some approaches were proposed which take into account the uncertainness of the values of the system parameters, the fuzziness of systems of differential equations, the inclusion of the derivative of the phase vector into the set of values of the right-hand part of equations of perturbed motion, etc. All those approaches are designed to take into account the fact that the real motion (the stable path) is imbedded into the set of other motions (paths) which occur under the action of unaccounted forces. N.G.Chetaev [1962] noticed that those “enveloping” motions, with an arbitrarily small difference from the stable motion, can be of oscillating nature, creating a kind of wave motion. Hence if the real motion is described by an ordinary differential equation or a system of such equations, then enveloping motions can be described both by ordinary differential equations and by equations with partial derivatives, e.g., Schredinger equations. Under the condition of connectedness of those equations, the obtained set of systems of equations is an example of a hybrid system.
