Models of socio-economic objects differ in the methods used to construct them. Accordingly, models can be static (with a stationary display structure of the original) or dynamic (with a variable display structure), statistical or deterministic, linear or non-linear, etc. These alternatives have fundamental differences

**Static and dynamic modeling**

Static modeling differs from dynamic in that it lacks a description of the change in the structure of the original over time. The static model uses the ratio of parameters that has developed at a certain moment, and it is assumed that this ratio does not change in time. In dynamic modeling, a significant part of the parameters is continuously changing. An important feature of dynamic modeling is the use of parameters that differently reflect resources: as flows, measured by the amount of resources per unit of time, and as accumulations, when the dimension is the amount of resources per se. For example, resource flows are the volume of production - units per year, revenue - thousands of rubles per year, average income of members of a social group - thousands of rubles per month, etc. Accumulations model resource reserves in pieces or tons, money in accounts in rubles or other currencies, etc.

In modern practice of economic calculations, static methods are widely used: linear and nonlinear programming, balance and other methods designed to find a solution for a short time interval. But at more remote intervals, such decisions are unacceptable. Attempts to circumvent the indicated drawback in various ways complicates mathematical calculations, but does not lead to correct results.

The method of dynamic modeling (MDM) is designed to study socio-economic processes and changes in states at unlimited time intervals and without reference to specific deadlines for the calculation. Moreover, during the simulation, all processes and states depend on control signals, external influences, the current structure of the model, which is determined both by the initial structure and the entire history of the object and its control until the moment the forecasting results are observed.

A dynamic model in its composition should always contain at least one dynamic element (integration or differentiation). In addition, an important feature of dynamic modeling is the possibility of implementing continuous processes in the model that are often not smooth (for example, stepwise). Static methods of calculations do not reveal rapid changes in parameters, which leads to noticeable errors in the results, while dynamic modeling allows you to reflect spasmodic changes in parameters, which significantly increases the correctness of the designed control.

**Statistical and deterministic models**

The separation of models into deterministic and statistical is performed based on the algorithms used. For statistical models, algorithms are based on past statistical indicators of socio-economic originals or “generate” signals using a random sampling of their values. Deterministic models are based on algorithms that reflect hypothetical dependencies (often tested by practice), as well as on heuristic algorithms, which are subsequently subject to validation.

When creating models of socio-economic objects, the use of statistical information is not always advisable, since it is often unique and generated by a unique set of reasons. In such cases, there is no representative information about a sufficient number of identical situations. This is due to the fact that unique and unsteady processes mainly occur in the economy and society. It follows that it is impossible to obtain the results of statistically independent events. In addition, if once in the past, on the basis of statistical methods, relations of parameters (for example, socio-economic) were obtained, then these relations can be transferred to the future only if the following conditions are met:

- models are built within the boundaries of the initial postulates of mathematical statistics;
- the simulated object (like the model) has a stationary structure of
- the relationships of elements.

Of the postulates of mathematical statistics, the following are important in this case:

- the number of tests should be so large that their increase does not change the results;
- all tests are carried out under the same conditions;
- test results should not affect each other;
- tests do not allow to reveal the causal dependence of the parameters, but only establish the tightness of the relationship between them.

Violation of at least one postulate of mathematical theory - and they are violated by any extrapolation of statistical data - in practice always leads to significant errors. Consequently, the application of the methods of mathematical statistics operating on random events is unacceptable for predicting processes in socio-economic objects and for preparing managerial decisions. Using a statistical analysis of the past for economic management is similar to driving a car in which the driver observes the traffic situation, looking not in the front, but in the rear view mirror.

As E.S. Birr, theorist and practitioner of the so-called “second wave” of cybernetics, once remarked: “... the concept of randomness is similar to the concept of unpredictability. The fact is that at least it can be argued that any event is unpredictable only insofar as we do not understand its causal mechanism. ” It follows that the more carefully the simulated object is described, the less random and, on the contrary, more definite (determined) should be in the description.

The statistical approach introduced the method of data extrapolation into economic practice. The indicators of past periods line up in a certain trend, which is extended into the future. The use of such a technique is unacceptable, since the indicators unreasonably change as if by themselves, without the influence of other factors. In fact, indicators do not change with time, but with the influence of various factors, which also obey certain laws. The mobile socio-economic structure in the past gives rise to the processes reflected in statistics, but in the future the structure changes, which creates a new nature of the processes. In the socio-economic object, only the general laws of the mutual influence of factors are preserved, and the structures of internal relations are subject to change. Statistics, therefore, reflects the state of an object only at certain moments in the past. When extrapolating, two errors are made:

- the stationary structure of the object is preserved, and from here it is unreasonably allowed to preserve the revealed patterns in the future by their nature and place of manifestation;
- the monolithic nature of the transformation algorithms inside a non-stationary object is affirmed, which by definition cannot be

Thus, statistical methods do not allow to obtain correct forecasts of the development of society, and deterministic methods open up the possibility of predicting future processes.

It is necessary to take into account at the same time that it is possible to express socio-economic laws only as a result of a statistical analysis of past events and causes. Only by summarizing a large number of phenomena and statistically analyzing the causes that caused them, we can describe some general dependencies. It is advisable to use the powerful mathematical apparatus of statistics to formalize socio-economic processes, taking into account various factors and relationships of phenomena.

Statistical information about the past only allows you to evaluate the ex post facto previously made management decisions. At the same time, if it is possible to reveal the essence of the relationship between the parameters of the object that have developed in the past, but are independent of time, then it becomes possible to find the laws of these connections, which, with certain reservations, can be used to build dynamic models. In addition, statistical data allows you to generate starting values of the parameters of the dynamic model to predict its future dynamics.

The deterministic approach in the dynamic modeling of socio-economic objects is based on hypotheses about the relationship between the parameters of the object and the initial structures of these connections. It should be remembered that the current rules of housekeeping may correspond to the objective laws of the operation of the facility, but may also hinder their manifestation. Therefore, one of the main tasks of modeling is to check the economic mechanism for adequacy to the laws of socio-economic development, as well as to identify time intervals when the directives of the economic mechanism are applicable.

During the simulation, it is often possible to detect unexpected changes in the model parameters. To find the reasons for these changes, it is necessary to repeatedly repeat the forecast on the model with the repetition of all previously performed managerial influences. In deterministic models, where there are no stochastic elements, the results of the previous simulation will always be repeated. This allows you to detect the place and time of occurrence in the root cause model of unexpected forecasting results, as well as determine the cause and effect chains of the translation of the root cause from the place and time of occurrence to the place and time of the manifestation of the unexpected result.

**Linear and nonlinear models**

When creating economic and mathematical models by traditional methods, the most attention is paid to linear methods of formalizing the properties of an object (linear programming, game theory, factor analysis, optimization methods, etc.). However, as the model becomes more detailed, linear reflection less and less meets the requirements of practice. In real life, linear relationships are virtually absent. As the experience of modeling socio-economic objects has shown, the presence in the model of even one constant coefficient over a long period of time always leads to the destruction of the original and its model. Therefore, constant regulatory values must be replaced in the model by variables.

For correct modeling, it is necessary to take into account the changing restrictions that apply to the flows of resources, production assets, opportunities, development rates, etc. In addition, it is very important to take into account the dynamics of the intensity and threshold of sensitivity of the model to various kinds of influences, the change in these influences and the influence of socio-psychological factors (addiction, fatigue, dependence of goals on time and condition of the object). Modeling should reflect a change in social, industrial and other structures. A mathematical description of the nonlinear relationships of the model, if formulated, does not present great difficulties. It is difficult to create a workable nonlinear model, since it requires long-term tuning, and its use is associated with a nontrivial search for the root causes of the resulting simulation results.

Structural changes constantly occur both in the nonlinear model and in the displayed object. Some internal connections disappear, others arise, so you can talk about a specific structure of the model only for a certain point in time, and at another moment the structure will change, that is, in essence, another model will arise. Structural changes depend not only on the original mathematical description of the original, but also largely on the modeled economic mechanism.

The economy is a purposeful activity of people in resource management, based on a comparison of projected acquisitions and loss of resources with the planned costs of resources necessary to achieve the goals. The goals themselves are constantly changing. For example, at first the economy needs to “survive”, then there is a need for “equal rights with competitors”, and then the goal is “leadership” in the market. Therefore, due to constant changes in the economic structure, management objectives, internal conditions and external influences, continuous interaction of the planning subsystem and the forecasting tool for creating a national economy strategy is necessary.

An economic forecast is necessary for the formation of a strategy for the economy to achieve a changing socio-economic goal, and a plan is necessary for the development of technology and resource management calculations based on the formed strategy for achieving the goal.

A dynamic model of a socio-economic object with many feedbacks, an unsteady structure and non-linear parameter transformations for an unprepared user appears to be a “black box” with random switching of model element relationships. But all changes in the structure of the dynamic model are completely determinate, and the emerging processes that look like random ones are actually deterministic, generated by a complex non-stationary structure, which changes according to non-linear but well-defined algorithms.

**DIN tool**

The DIN tool is designed to predict trouble with any control option. The purpose of its application is the search for management strategies that do not allow crises. Using DIN, the dynamics of complex nonlinear economic objects with unsteady architecture and many feedbacks is modeled. Prediction is performed on models that are connected systems of nonlinear differential equations with feedbacks, some of which develop the economy, while others destroy it.

Modeling practice has shown that for models - and, therefore, for real objects - long-term acceleration is most detrimental. If acceleration occurs even in a single parameter for one year or longer, the model begins to “fall apart”. Acceleration “infects” other parameters, activating positive feedbacks in the model. The avalanche of acceleration very soon becomes impossible to stop due to the redistribution of resources, and there is an economic collapse. If they arose, then sometimes you can suspend them only by changing the structure of the economy. In this case, a very effective change is the strengthening of the planned start in the economy. A crisis-free economy arises when the necessary balance of market and planning mechanisms is achieved.

Thus, it is extremely important to be able to predict accelerations and find their causes. The DIN tool is needed to prevent disasters. It is required to predict the causes of prolonged accelerations.

In a “quietly” developing system (without crises), a constantly changing balance must be observed not only between the number of positive and negative feedbacks, but also the balance of the intensities of the effects of these connections. In the DIN system, automatic algorithms (economic “autopilots”) that control feedback signals are often used for such a balance, which contributes to the crisis-free conservative development, i.e. economic development at a constant speed without prolonged acceleration.

DIN provides for the creation of models in order to correctly reflect existing socio-economic systems. Any relationships between the individual model variables should be verifiable and justified - in particular, reflect relationships of parameters similar to the interaction of objects and phenomena in real life. Built-in control algorithms redistribute resources and change economic structures over time according to the criterion of preventing a crisis. They reproduce a complex of economic, financial, social, political and other structures, the changes of which give rise to not obvious situations in the future. At any step of the forecast, management parameters can be changed, thereby simulating the proposed steps for managing the real economy.

The purpose of the use of DIN is to find management strategies that do not allow prolonged crises. Using DIN, the dynamics of socio-economic objects, which are characterized as:

- complex (generating chaos);
- nonlinear (with changing signal conversion operations);
- dynamic modeling changes in the velocities and accelerations of the parameters of objects that have a changing (non-stationary) structure (architecture) and contain many cybernetic feedbacks (positive and negative), as well as many cross-talks (which are not cybernetic feedbacks).

The analysis of the forecasting results shows that it is impossible to obtain satisfactory results at large time intervals with one control lever. Continuous control of many levers is necessary, and, most importantly, a correct “selection” of time points, sequence and intensity of application of each control lever is necessary. Moreover, one should bear in mind the unequal sensitivity of the nonlinear dynamic system to control actions at different time intervals of its “life”, it will always be different.

The results of using the DIN tool are not future states of socio-economic objects, but forecasts of changes in the parameters of these objects (forecasts of changes in speeds and accelerations of parameters and changes in economic structures) under the influence of managerial decisions and external influences. At the same time, based on the predicted data, it is possible to evaluate the effectiveness of decisions in a comprehensive manner, taking into account both the direct responses of the affected object and the indirect consequences for other objects, as well as, very importantly, not only the immediate, but also the long-term consequences of decisions made over the entire forecasting interval.

Based on the use of DIN, it is provided:

- testing economic development programs, as well as certain important decisions within the boundaries of available resources and estimated external impacts, the search for crisis-free macroeconomic management strategies under external (international) impacts;
- forecasting (from 1 year to 5-10 years) of the implementation of socio-economic development programs, including economic and military-political interaction with other countries;
- training in skills and techniques for managing the dynamics of economic objects using simulators, standard modules and economic reflection algorithms. Management is implemented by the “levers” of economic, financial, social, and other objects available in real life that are reflected in the models;
- business games in the form of training and an economic practical work on conducting business in a market with competition or cooperation (business games of several participants, where market algorithms and consumer behavior of business results are modeled on a computer and the business is managed by players);
- testing company staff for their promotion or at contests for filling vacancies.

To predict the socio-economic dynamics, there are:

- system (software) and technology for dynamic modeling of predicted objects DIN;
- methods of dynamic modeling of the system, non-linear, differential equations with non-stationary structure and many different feedbacks (this simulation allows to obtain deterministic chaotic processes, i.e. completely unexpected changes in future dynamics);
- special unique interface for simultaneous control of the model using numerous control parameters and monitoring the predicted results;
- extensive (over 40 years) experience in similar developments;

More than 10 published monographs describing the synthesis of economic and mathematical models of extra high complexity.

Din tool correctly reflect future dynamics

- production processes
- living standards of social groups (both in the country for which model forecasts are made and in other countries),

social tension index, - demographic and migration changes and their consequences,

the public education system (secondary school, secondary and higher education, retraining of existing workers, etc.), - defense industry
- foreign trade
- all the contours of financial dynamics interconnected (taxes, loans, prices, inflation, foreign exchange exchanges, etc., many other parameters and indicators that may change as a result of the proposed management impact),
- the root causes of the creation and collapse of international coalitions (unions, blocs, etc.) and the impact of these processes on the national economy.

In addition, there are several dozens of “standard” (source) model modules (that is, model models) that can be refined to the level of working models. Such source modules include, for example, dynamics models:

- market pricing of goods in the sales market;
- the phenomenon of fashion for something (goods, music, politics, etc.);
- competition of commercial banks;
- exchange rate of the national currency;
- external and internal labor migration;

parameters of social groups of the population (standard of living, quality of life, social tension, unemployment, degree of satisfaction with one's economic condition, level of financial savings in banks, intelligence index, share of paid leisure time, index of need for household services, housing security index, and much more) ; - a continuous change in the coefficient of elasticity of demand for a product from a change in its price, taking into account the multitude of continuously changing external market conditions.

Based on the use of DIN, it is provided:

- testing economic development programs, as well as certain important decisions within the boundaries of available resources and estimated external impacts, the search for crisis-free macroeconomic management strategies under external (international) impacts;
- forecasting (from 1 year to 5-10 years) of the implementation of socio-economic development programs, including economic and military-political interaction with other countries;
- training in skills and techniques for managing the dynamics of economic objects using simulators, standard modules and economic reflection algorithms. Management is implemented by the “levers” of economic, financial, social, and other objects available in real life that are reflected in the models;
- training in the form of business games and an economic practical work on doing business in a market with competition or cooperation (business games of several participants, where market algorithms and consumer behavior of business results are modeled on a computer and the business is managed by players);
- testing company staff for their promotion or at contests for filling vacancies.