Forecasting the development of the industrial complex: Southern Federal District

Models of global dynamics are currently being developed, such as mathematical modeling and management of the dynamics of development of regional socio-economic systems based on the ideas and theories of synergetics [8, 29], in cognitive modeling (2–7, 22, 26, 30–34).

As for the consideration of problems of planning socio-economic systems, the works of the following researchers were considered.

Gumerov [16] studied the economic and political aspects of the development of planning in the USSR, formulating the basic requirements for the ideology of strategic planning and management, and noting that the activity was reduced to formal changes in the regulatory framework and methodological support. Shafranskaya [35] notes that in the current conditions, it is necessary to build a full-scale strategic planning system. As Professor Orlenko [27] notes, we can consider the experience of implementing planned activities in Yugoslavia. Kryukov and Seliverstov [21] conducted an analysis of the draft strategy for the Socio-economic Development of the Siberian Federal District until 2035, and identified a number of shortcomings associated with systemic problems in regional development planning. One of the solutions is the use of a variable format for the development of the coal cluster, that is, the development of scenarios for existing and future trends in economic development.

Krupkina et al. [20] considered the issues of forecasting Russia's GDP using a structural factor model (DFM). The use of this model showed more stable results of GDP forecasting over time. The authors also point out that for a more effective forecast, it is better to give preference to models that also take into account the inverse relationship between variables.

Lazhentsev [24] considered the understanding of the “program-target method” as a scientific category that allows us to separate the objective causes of the mobilization economy from its reflexive interpretation. The author notes that a scientifically objective assessment of the current situation leads to solving the problems of long-term technological development.

Kleiner et al. [19] propose to use versions of strategic planning, taking into account the state of economic theory, economic policy, and the peculiarities of the functioning of the Russian economy.

A review of the scientific literature shows the increasing importance of planning issues for the development of economic entities, but insufficient attention is paid to the use of digital forecasting tools. Domestic and foreign research devoted to making forecasts using the cognitive modeling method deserves much attention.

Li and Chiang [11] studied the intelligent forecasting of financial time series based on a neurofuzzy approach with multiswarm intelligence. Applying CFS to CNFS can increase the adaptive capabilities of non-linear function mapping, which is valuable for non-linear forecasting. Istvan and Laszlo [18] studied fuzzy cognitive maps (FCMs), defining them as recurrent neural networks that are used to model complex systems using weighted cause-and-effect relationships.

Kwilinski and Kuzior [1] mention in their article about the theory of cognitive modeling for the development of industrial enterprises, but the article does not present real cognitive models for the development of industrial enterprises. Bąk and Cheba [9] present in their article the results of modeling a complex economic system of a country in order to achieve sustainable development goals. However, the article does not present scenarios of system behavior when exposed to the system under study.

Gorelova et al. [15] explore issues of cognitive modeling of socio-economic regional systems, which allowed them to propose development models for the Republic of Adygea in the context of the Granberg regional development model. However, these works did not consider the issues of cognitive modeling of certain industries or types of economic activity. The models they developed provide directions for the development of the socio-economic systems under study, which can be used to make management decisions on the development of the region.

Kulba [23] proposed the construction of cognitive maps by using the method of summing the increments of factors. Maksimov [25] proposed a scenario analysis framework for cognitive modeling. Thus, there are different understandings in the planning tools for the development of weakly structured socio-economic systems.

Therefore, it is proposed to use a scenario-based approach using cognitive modeling to study forecasting the development of the industrial complex, since its application is possible without specific quantitative data. Thus, there are no works devoted to the construction of forecasts for the development of industry in the Southern Federal District. Gorelova G.V. worked in terms of forecasting the development of the subject – Adygea. Her forecasts were based on the use of cognitive modeling method. The analysis of statistical collections [17] has shown the absence of the necessary amount of data to build forecasts of industrial output using mathematical methods – exponential smoothing. Therefore, to build forecasts for industrial development, tools based on fuzzy logic were used – cognitive modeling, which does not require a large array of quantitative data of the predicted processes. The term “cognitive maps” was first proposed in 1948 by the American psychologist Tolman [37] in his work, “Cognitive maps in rats and humans”. The development of this cognitive methodology was mainly due to the work of Atkin [7], Casti [10] and Roberts [30] [8]. We used the authors’ concept of cognitive data modeling.

Using formula 1 and computer program [28], a cognitive map of the industry of the Southern Federal District was built (Figure 1). This cognitive map is a model of industrial development. It is impractical to reduce the number of vertices, since some types of industry will be absent. The cognitive map was built using a program that used formula (1) to build vertices (V_i) and connections E between them.

Stability analysis is directly related to the analysis of the processes of propagation of disturbances according to the concepts of the cognitive map. Let some changes begin at vertex 1, for example, the growth of industry in the Rostov region. The influence spreads along the routes M1 = {e12, e13, e14}. As you can see, an increase in the X1 indicator along the M1 route leads to an increase in 1. At a certain point in time, due to these oppositely directed processes, an equilibrium must occur between the vertices.

A qualitative analysis of routes and cycles does not reveal the full depth of the processes taking place in a real system. A further generalization may be to assign to each vertex i a numerical value Xi, i = 1,2, …, k and introduce the intensivity of the connection between vertices i and j as a function of f(i, j).

Under the influence of various perturbations, the values of variables at the vertices of the graph can change; a signal received from one of the vertices propagates along the chain to the rest, amplifying or fading.

In general, if there are several vertices j adjacent to j, the process of perturbation propagation along the graph is determined by the rule: (2) xi(t+1)=xi(t)+=f(xi,xj,aij)pj(t) {x_i}(t + 1) = {x_i}(t) + = f({x_i},{x_j},{a_{ij}}){p_j}(t)

Modeling can be carried out in steps or pulses.

The essence of such modeling is that a certain change is set at one of the vertices of the graph. This vertex actualizes the entire system of indicators, that is, the vertices associated with it, to a greater or lesser extent.

The second stage of cognitive modeling is the study of the properties of a complex system on a cognitive model, such as resistance to disturbances, structural stability, paths, cycles, complexity, connectivity, sensitivity, dynamics, and simplicial analysis.

The program was used to make forecasts [28] and formula (2). Figure 2 shows the results of calculating the eigenvalues of the adjacency matrix of the model G. The determination of the roots of the characteristic equation is necessary to analyze the stability of the system to disturbances and by the initial value. In this case, the stability criterion M < 1 is used, and M is the maximum modulo of the corresponding number (the root of the characteristic equation of the matrix) [12]. Since in this case M = 3.69 > 1, the Kranet system G is unstable neither to perturbations nor to the initial value.

Figure 2:

The third stage of cognitive modeling is scenario analysis, carried out using pulse modeling [14, 16]. It makes it possible to significantly expand the possibilities of using indicators of industrial development and indicators of its components, and causal analysis is a methodology for the scientific analysis of these phenomena and processes.

Impulse modeling can be used to further simulate the development of the situation [13]: (3) xi(n+1)=xvi(n)+∑j=1k−1fijPj(n)+Qi(n) {x_i}(n + 1) = {x_{vi}}(n) + \sum\limits_{j = 1}^{k - 1} {{f_{ij}}{P_j}(n) + {Q_i}(n)} Where:

x_i(n) – the value of the impulse in the vertex V_i at the previous moment-stroke of modeling n;

When it is difficult to quantify the x_i(n) then the x_i(n) = 1, P_j(n) = 1 will be accepted [10].

The program was used to make forecasts [28]. As can be seen from Figures 3 and 4, when implementing programs aimed at improving the industry of the Rostov region, its industry will begin to develop rapidly. Pulse modeling was used for further modeling [23]. Since it is impossible to quantify the results of the influence of factors, according to the theory of cognitive modeling, impulse influence +1 is considered (there is an influence); – 1 (no impact).

Figure 3:

Figure 4:

To obtain forecasts of the development of the situation using cognitive maps, the method with summation of factor increments is used in this work [23]. Possible scenarios for the development of the system are considered in the example of the industry of the Rostov region – scenario 1 and the Krasnodar Territory – scenario 2, as subjects of the federal district, where the widest range of industries are represented and which were selected to determine the first scenario options. These scenarios are preliminary scenarios for a given set of factors.

Scenario #1. Let the program to increase the industry indicators of the Rostov region be implemented, the control pulse q40 = + 1 (q40 – vertices in Table 1); the perturbation vector Q = {q₄₀ = + 1}. The simulation results are presented in Figures 3 and 4.

Scenario #2. Let the program to increase the indicators of the Krasnodar Territory industry be implemented: the control q₄₆ = + 1 (q₄₆ – vertices in Table 1) and the perturbation vector Q = {q₄₆ = + 1}. The simulation results are presented in Figures 5 and 6.

Figure 5:

Figure 6:

As can be seen from Figures 5 and 6, when implementing programs aimed at improving the industry of the Krasnodar Territory, its industry will begin to develop rapidly, and positively affect the industry of the region as a whole.

The results of the scenario analysis indicate the need to make decisions corresponding to these trends, which should have a positive impact on changes in target factors. The development model of the industrial complex of the Southern Federal District has shown that the industry of the district is in an unstable state.