**MODELLING in cybernetics** — the way of studying of various objects, processes and the phenomena based on use of the models representing or physical analogs (physical modeling), or the formalized descriptions of a body of interest (mathematical modeling).

Physical. The m allows to replace natural experiments with studying them physical. models, especially when the experiment cannot be conducted or due to the lack of an object at a stage of its design, or because of danger of experiments in actual practice (e.g., in medicine).

The main condition of M. is the preservation of certain ratios of similarity between the original and model providing compliance of the data obtained on model with data on a real object. Only in this case M. can form a basis for receiving reliable data about a body of interest.

Physical. The m is widely used in medicine. In particular, creation of models of bodies — an indispensable stage of creation practically any artificial organ (see. Artificial organs ) or subsystems of a live organism.

Broad use has mathematical M., i.e. creation of the accurate formalized (mathematical) description of a body of interest. Creation of mathematical models is carried out when there is an opportunity to connect by mathematical ratios (formulas, functional dependences) the key parameters of a body of interest and condition defining a possibility of its functioning.

At creation of mathematical models only major factors, characteristic patterns of the described phenomena are taken into account and minor and unimportant factors are discarded.

Mathematical models are under construction on the basis of informative descriptions of data on physical. the nature and quantitative characteristics of a body of interest, about degree and the nature of interaction between separate elements of an object and about the place of each element in the general process of functioning of an object. In turn, informative descriptions can be under construction on the basis of observations and fixings of quantitative characteristics during the carrying out the corresponding researches by means of the available equipment and the equipment. In the absence of the equipment of the informative description syntheses of the available experience are the cornerstone, of results of overseeing by functioning of similar objects, processing of statistical material, theoretical analyses. The informative descriptions forming a basis for M. are carried out by specialists of that specific area, to a cut the studied objects (doctors, physiologists, biologists, engineers, economists, organizers of health care etc.) belong.

Further on the basis of the informative description of process (object) creation of the formalized scheme and direct mathematical is made by M.

The formalized scheme represents an accurate statement of the list and interrelations between all elements of the studied objects, their numerical values (including — limits of changes). These values can be generalized in the form of tables, schedules, and interrelation — in the form of flowcharts.

The formalized scheme is under construction when direct transition from the informative description to mathematical M. is complicated. Such scheme jointly by specialists of the corresponding application area of knowledge and mathematics, and mathematical model — as a rule, the mathematicians having the informative description is developed. At M. of objects of wildlife in view of their extreme complexity various assumptions and idealization are used that considerably facilitates studying of such objects and gives useful information for the organization and carrying out more in-depth studies. E.g., at a nek-swarm of idealization the live brain and universal digital cars can be carried to the same class of dynamic systems, and their functioning can be described by similar mathematical models.

The look and the nature of the mathematical expressions which are models of bodies of interest is defined by properties and character of these objects. Therefore at creation of mathematical models of real objects use the most various sections of modern mathematics: variation statistics (see), the functional analysis and linear programming (at problem solving, the extreme modes connected with stay), theories of turns and the theory of mass service (during the modeling of systems of service), laws of probability (at problem solving, idiosyncrasy to-rykh is accidental character of the studied phenomena), theories of games (at problem solving, several systems connected with adoption of the optimal solution in the conditions of interaction) etc. Use of computer facilities considerably expands possibilities of mathematical M. The matter is that a class of the equations which can be solved analytically it is considerable already a class of the equations solved by means of approximate numerical methods. Use of digital computers allows to automate calculations if for the decision the corresponding numerical approximate methods are used. In addition to digital computers, analog cars (the car of continuous action) are used to modeling. The principle of operation of analog machines is based on analogy between electric, hydraulic, thermal and other phenomena. At the same time the valid process analog is replaced with the processes happening in electronic circuits of the analog car and described by the same equations as the modelled process. Therefore cars of continuous action are called also modeling installations. The modeling cars are capable to imitate the most various phenomena physical. the nature provided that they can be expressed by the corresponding equations.

M of work of a brain, separate bodies and systems biol. objects, activity of a health system it is widely used for deeper understanding of the processes happening in a live organism, definitions of ways of improvement of the medical help to the population, developments of new methods of treatment for the solution of other tasks.

M.'s use in medicine makes one of the main problems of medical cybernetics (see. Cybernetics medical ).

See also Mathematical methods (in medicine) .

**Bibliography:** Antomonov Yu. G. Modeling of biological systems, Reference book, Kiev, 1977; Buslenko V. N. Automation of imitating modeling of complex systems, M., 1977, bibliogr.; Modeling in biology and medicine, under the editorship of D. A. Biryukov and G. I. Tsaregorodtsev, L., 1969.

*O. I. Aven.*