Hard and soft mathematical models and their applications

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Ohirko I. V., Yasinska-Darmi L. M., Yasinskyi M. F. № 1 (50) 107-122 Image Image

One of important scientific problems of natural history is to solve a task of foresight of the probed object conduct in time and space on the basis of certain knowledge about its initial state. This task has been taken to find some law which allows to define the object future in any moment of time of t>t0 with the initial moment of time of t0 in the point of space of x0. Depending on the degree of the object complication the law can be determined or probable, it can describe the evolution of object only in time, only in space, and can describe a spatial-temporal evolution. Under the dynamic system they understand any object or process, for which a simple certain concept of state as some totality of values has been determined in this moment of time, and the law which describes time history (evolution) of the initial state has been set. The mathematical model of the dynamic system is considered to be set if the system parameters (coordinates) have been introduced to determine its state simply, and the law of evolution has been detected. Depending on the degree of approaching, different mathematical models can be put in accordance with the same system.

Keywords: system, dynamic systems, soft systems, hard systems, linear operator.


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