Fractal formalism in identification of indoor sports facilities as systems with partial indeterminism

Abstract

The paper considers the peculiarities of functioning and management of closed-type sports facilities designed to implement artificial hypoxic training process. For identification of such complex systems models of different types are used depending on the goals set. The complexity of the choice of physical and mathematical models in this case is due to the complexity of the behavior of the systems under consideration at different moments of time, during which their basic properties can change dramatically. The use of the E. Lorentz air carousel allows in this study to apply the methods of fractal formalism and modeling to describe the behavior of such numerically irreducible systems. An algorithm for determining the self-similarity region for the object under study is given, which, in its turn, makes it possible to reduce the probability of violation of its normal operation mode, namely, maintaining the constancy of static and dynamic components of oxygen partial pressure, proper humidity, speed and direction of air mass flow circulation in the given structure (without using energy-consuming forced ventilation system). The possibilities of application of fractal models and methods of geometrical control theory for identification of complex systems/sports facilities of the closed type functioning in energy-saving modes and intended for artificial hypoxic training are considered.  

It should be noted that for air mass circulation technologies (without the use of forced ventilation) in closed sports facilities for hypoxic training of athletes, the above method of determining the self-similarity region can serve as an analogue of the indicator, which constantly registers the approach of the determining parameter to one of the boundaries of the self-similarity region, thereby signaling the probability of a situation that leads to a sharp change in the direction of circulation of air masses in the building.