Evolution models of quasiattractors of anthropometric parameters of pupils of Ugra and Bashkortostan republic

Abstract

The evolution of biological systems on the example of changes in anthropometric indicators of the three age groups of pupils Ugra and Bashkortostan Republic from the perspective of theory of chaos and self-organization is considered. The kinematic parameters of complex systems (systems of third type) based on the motion simulation system of the state vector x(t) in the phase space of state were calculated. A special mathematical apparatus for calculation of the centers of quasi-attractors (areas of phase space in which x(t) changes continuously) and the rate of evolution was used. The authors demonstrated the calculations of the quasi-attractors’ volumes, the coordinates of their centers, as well as the velocity of these centers and the rate of evolution of biological systems in the phase space of states. A comparative analysis of the kinematic characteristics of students of Ugra and Bashkortostan Republic showed significant differences in the dynamics of anthropometric parameters.