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Classification of mathematical model

The building basis of the model is a class of models suggested in [9]. The main feature of this class - research and modelling of oscillatory and periodical processes in the modelling object. Our model is self-adapted, it reflects the most important homeostatic [7] features of the blood circulation system.

In outlook the model of this class is represented as a dynamic system

(1)

where

i= 1,…,n ( n – system dimension),

j = 1,…,l (l– total number of system descriptions),

A = (A1,…,Ar) – vector of parametres with dimension r,

some nonlinear functions Xij describe an object in different phases of cardiac cycle. The jump from p- description to q-description

of equations system (1) takes place after satisfaction of p-q-jump conditions

(2)

In the moment of jump tpq new values of condition variables are calculated through the values of old condition variables by means of sliding movement equations

(3)

The dynamic system describing with (1) - (3) is non-autonomy, because time variable t is included in jump conditions (2). The satisfaction of p-q-jumps means, that the modelling object is being described by different systems of differential equations in different phases of cardiac cycle (systole, diastole) .


Mathematical model > Classification

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