Y.P. Mukha, V.I. Sloogin

Functioning of functional systems (FS) in interaction with the involved systems on the basis of structural formalization for the purpose of studying of dynamics of process of functioning is considered. Difficulties of studying are connected with absence of receptions of representation FS in phase space depending on time parameter. The teoretiko-plural approach and a mathematical apparatus of the description of functioning FS by means of categories of time dynamic systems and concept of system time is offered. It is given category model of family of categories FS SAP. The functional family of categories of work of heart (WH) on the basis of structure of following of potentials of action of heart-s spending system and formalisation of fragments of metabolism process of a cardiac muscle is considered. On the basis of functional families of category FS SAP and WH their time categories which are taken as a principle experiment techniques on studying of function of dynamic interaction of functional systems. Results of the spent experiment have allowed to draw a conclusion on essential nonlinearity of process of interaction of functional systems. Zones of conformity of average dynamic pressure (ADP) and frequency of warm reductions (FWR) are thus allocated: on different intervals FWR of speed of change ADP different at all groups of examinees. It allows to estimate interval adequacy of heart-s work to loading growth. As a result it is noticed that structural formalisation is mathematical base of consideration of the independent and connected behaviour of functional systems of maintenance of arterial pressure and heart work. Thus dynamic pair (SAP, WH) has the multilayered enclosed structure of adaptive interaction within the limits of interaction.