Sustainable development of ecological, economic and socio-humanitarian systems is a crucial challenge in the modern world of instability and crises. To address this challenge, integrated models based on mathematical methods, models and innovative technologies are needed to manage and predict the nonlinear dynamics of these systems. Moreover, these models should incorporate humanitarian and cognitive variables that afect the behavior and decision-making of the system agents. In this paper, we present and develop a cognitive approach to modeling sustainable development of complex technogenic production systems in the innovation economy. We propose an integration model of sustainable development as a family of models for creating integrated information systems of ecological, economic and socio-humanitarian management of various social and organizational systems, especially economic objects of anthropogenic nature. We also present a cognitive model of nonlinear system dynamics that takes into account the dynamics of the humanitarian component with management in general. Furthermore, we introduce a model of innovation capital dynamics for the eco-economic and socio-humanitarian system (EESHS), as innovation capital is broader than intellectual capital by its nature and content. We derive an extended integral model of nonlinear stochastic dynamics of EESHS in the innovation space. The theoretical foundations and paradigms of our research are based on: systems of type “X”, integral models and the problem of sustainable development, models such as “NMSSD” and systems such as “SEEHS”, convergent technologies “NBIC” and “NBIC⊕ SG”.
Sustainable development is defined as “development that meets the needs of the present without
compromising the ability of future generations to meet their own needs” [
The United Nations has adopted 17 Sustainable Development Goals (SDGs) as part of the
2030 Agenda for Sustainable Development, which sets out a 15-year plan to achieve them [
One of the key challenges for achieving sustainable development is to understand and
manage the complex dynamics of ecological, economic and socio-humanitarian systems in the
modern conditions of instability and crises. These systems are characterized by nonlinearity,
uncertainty, feedback loops, emergent properties, self-organization and adaptation [
Moreover, these models should take into account not only the physical and material aspects
of the systems, but also the humanitarian and cognitive aspects that afect the behavior and
decision-making of the system agents. Humanitarian factors include ethical, moral, legal, social
and psychological dimensions that shape the attitudes, values and preferences of individuals and
groups [
In this paper, we present and develop a cognitive approach to modeling sustainable
development of complex technogenic production systems in the innovation economy. A technogenic
production system is a system that consists of human-made elements such as machines, tools,
materials, products and processes that interact with natural elements such as resources, energy
and environment to produce goods or services. An innovation economy is an economy that is
driven by technological innovations that create new products or services or improve existing
ones [
The main contributions of this paper are extension of the results presented earlier in [
Currently, the determining factors of a knowledge-intensive enterprise (KE) are not so much production capacity, but rather knowledge, know-how, research and development.
The theory of production factors (PF) by the beginning of the 21st century became one of the
actual research directions, covering the methodology of economic analysis and management
of economic subjects. The main postulate of the theory of production factors is that the ratio
of external factors of production and the internal state of the economic entity determines its
strategic position in a complex and multidimensional market space, i.e. its organizational,
economic and structural sustainability [
The main provisions of the modern theory of PF can be formulated as follows: organizational and economic sustainability of the economic entity is determined by the ratio of available factors of production and their efective management; competitive advantages of the economic entity depend on the availability (including ownership) of strategic resources; efective management of available factors of production is provided by organizational capabilities of KE; taking into account cognitive, stochastic, humanitarian and “NOT-” factors.
A logical question arises: what properties should the factors of production have, so that the innovative development of the KE could be efective, intensive and adaptive?
To answer this question, it is necessary to clarify the list of PF, which play a key role for the sustainable functioning and development of KEs, to introduce the concept and give a definition of cognitive factors of production; to develop a classification of cognitive factors of production, etc.
To implement this task, we will use the system paradigm, analyze the known concepts of
PF and identify the main characteristics of cognitive production factors, which determine the
organizational and economic sustainability of KE1 (figure 1) [
Cognitive production factors (CPF). The analysis of the development of the theory of production factors and the emergence of their new types shows that the composition and role of production factors are most closely connected both with changes in production itself, and with the development of economic science, identifying and explaining the emergence and purpose of certain production factors by increasing opportunities for economic growth of knowledge-intensive enterprise.
Thus, according to the theory of human capital (the term was introduced by G. Becker
[
By its economic essence, human capital is closer to the intangible fixed assets of an enterprise. According to the theory of human capital, investments in human beings are regarded as a source of economic development, no less important than “ordinary” capital investments. This means that an economic dimension is applied to a person.
The modern stage of KE development is characterized by qualitative changes in the types of socially significant human activity: labor characteristic of an industrial society is replaced by creativity in a post-industrial society. Machine technology gives way to “intellectual technology”. As a result, knowledge and information become the leading factors of production, which leads to a decrease in the role of material factors of production. Radical changes in production relations have led to special requirements for the quality of human resources, highlighting their intellectual component and making them an independent factor of production.
Let us introduce the concept of cognitive production factor (CPF) – it is an embodied in an economic entity totality of knowledge, abilities, skills, which contribute to the growth of human productive power in the creation of an intellectual product demanded by the market.
The convergence of intellectual resources and information technology as a productive force causes the emergence of new types of factors of production – cognitive production factors (CPF, ) – which means specific, dificult to imitate resources of an industrial enterprise to create a product and added value, demanded by the market.
CPF are considered as a productive force arising from the convergence of human cognitive abilities and information technology.
Cognition as a scientific-cognitive action, is moving to a new quality, providing relevant
knowledge for complex research. Artificial intelligence, neurocomputers, technologies of various
interfaces based on the use of the properties of the human brain [
CPF provide internal (endogenous) opportunities for the development of industrial
enterprises and, in fact, become one of the sources of endogenous economic growth [
The allocation of CPF as a new type of productive force necessitates the development of appropriate methods and models of their management, the practical implementation of which is possible due to the mechanism of integration into the overall management circuit of the industrial enterprise.
The efectiveness of methods used in the management of traditional factors of production is becoming less efective, since it does not take into account the dynamics of modern changes, the need to process a large amount of data, the structural complexity of management tasks, the need to use coordination mechanisms.
The study of theoretical and practical results of production factor management allowed us to conclude that CPF management should be integrated into the overall management circuit of a high-tech enterprise and be supported primarily by end-to-end activities implemented through appropriate business processes.
The increasing intellectualization of industrial production contributes to the fact that the
distinctive features of enterprises become:
• significant individualization of products in conditions of high flexibility of high-volume
production;
• the modern vector of civilizational development of society is represented by the intensive
spread of global technologies: nano-, bio-, information and communication technologies.
Cognitive technologies refer to the technologies of the global level, the transformative
efect of which gives a new quality of interacting elements and leads to the formation of
a fundamentally new technological platform for economic development;
• integration of consumers and manufacturers in end-to-end processes of the entire product
lifecycle and value chain;
• integration of information and data within production networks, reflecting all aspects
of requirements, design, development, production, logistics, operation, service, etc., i.e.
creation of “production intelligence”;
• globalization of product/goods development teams, as the complexity of products requires
a variety of competencies;
• formation of a networked production “ecosystem” through cooperation and reduction of
barriers between enterprises and customers;
• development of cloud technologies as a way to implement customized production on
demand; use the production capabilities of virtual production networks based on united
production sites, and support them with special software;
• isolation and accumulation of intangible functions, such as research and forecasting
of the market and demand, formation of the product concept, formation of technical
requirements, etc.; since intangible components take an increasing share in the cost and
price of the finished product;
• formation of the market value of enterprises due to the knowledge of employees,
knowhow, knowledge-intensive technologies, inventions, industrial designs and other
intangible assets. The qualitative change of production factors puts forward a set of interrelated
tasks for industrial enterprises [
Thus, sustainable economic growth and development of modern industrial enterprises determines not so much the number of personnel, but the presence of workers who are able to conduct scientific and technological development at the modern level, to create competitive products and services on their basis, to propose new ways of organizing production, to determine the process of forming new trends in technological development in the market environment. In this regard, we need a diferent system of productive forces, surpassing the capabilities of industrial type of production and other ways of combining human and material labor.
The convergence of intellectual resources and information technologies as a productive force causes the emergence of new types of production factors – cognitive factors of production – which are understood as specific, dificult to imitate resources of an industrial enterprise that allow creating a product that is in demand by the market.
Cognitiveness, as a scientific and cognitive action, is moving into a new quality, providing appropriate knowledge for comprehensive research. Artificial intelligence, neurocomputers, technologies of various interfaces based on the use of the properties of the human brain are a fundamentally new environment for human production activities. The use of cognitive principles in the economy allows you to bring the main production processes to an intellectually new level.
Cognitive production factors provide internal opportunities for the development of industrial
enterprises and, in fact, become one of the sources of endogenous economic growth [
The identification of cognitive factors of production as a new type of productive force
necessitates the development of appropriate methods and models of their management, the
practical implementation of which is possible due to the mechanism of integration into the
overall control loop of an industrial enterprise [
So, cognitive production factors (CPF, ) – are the result of the convergence of intellectual resources / intellectual capital and information technology:
“IR/IC” & “IT”, where & – here is a conditional symbol of convergence.
Cognitive basis of high-tech activity, which includes the unity of knowledge, experience, creativity and information technology. Structural elements of CPF are: knowledge, experience, creativity and skills in the use of information technology, i.e. CPF – is a tuple <knowledge, experience, creativity, level of use of IT, ...>.
One of the variants of correlations of cognitive production factors (CPF), human capital (HC) and intellectual capital (IC) by three comparison parameters.
1. Structural elements: 2. Methods of evaluation and measurement: • CPF: Knowledge, experience, creativity, skills, in the use of information systems and technology. • HC: Level of education, health status. • IC: Market assets, human assets, intellectual property, infrastructure assets. • CPF: Indicator based on up-to-date financial and accounting statements. • HC: Aggregated indices, the calculation of which requires an extensive information base.
• IC: Ratio of market value to book value; Intellectual coeficient of value added. 3. Correlation with performance results: • CPF: Production function. • HC: The balanced scorecard system. • IC: Aggregate of IC and capital involved.
Note that the presented list of CPF is not exhaustive, it can and should be supplemented and improved.
So, CPF is a set of both active and intensional, as well as tangible and intangible factors of production: • tangible-active can include those CPF, which are embodied and directly used in the economic turnover. These include local computer networks for information exchange, lfexible manufacturing systems (FMS), simple/complex robots, automated information storage and retrieval systems, planning systems (ERPI, ERPII), design systems (CFD, CAE, PLM), electronic document management systems, vision systems; • intangible assets include objects of intellectual property: know-how, technical solutions, licenses, patents, databases, information about customers and suppliers, etc; • material-intentional cognitive factors include the potential use of advanced technologies, such as augmented reality technologies, artificial intelligence technologies: Internet of Things technologies, big data, cloud computing, deep learning, 5G, etc; • intangible-intentional include personal characteristics of employees, experience, culture of thinking, ability to learn, creativity, insight, intuition, level of education, level of digital literacy, ability to cognitive activity, analysis, reflection, self-regulation, communication abilities, compliance with ethical and social norms.
Let us also note now that innovation capital is one of the most important and specific forms of capital, reflecting the ability of industrial enterprises as participants in the innovation cluster to generate income due to the development of innovative activity and acquisition of a special status due to the dynamics of innovation potential as an institution capable of transformation into capital as a result of the synergistic efect of interaction between economic entities in the process of innovation development. Innovation capital from the point of view of classical economic theory is characterized by three essential features, namely, it is a product of past labor, the role of which is played by innovation potential; it is a production or product stock in the form of innovations produced and ready for implementation, as well as innovations requiring further improvement and innovations that can be accumulated in the form of innovation potential; it is a source of income based on the efective commercialization of innovation [29, 30].
By its nature and content, innovation capital is wider than intellectual capital, which
according to the concept presented in the works of Milner [
Let us present a cognitive model of the nonlinear dynamics of the system, taking into account
the dynamics of the humanitarian component with control (as an extension of the integral
model [
In equations (1)-(3) the variable () is a humanitarian variable, () – cognitive
variable, () – variable (level) of innovativeness in the integral model EESHS [
So, supplementing the system of equations of the integral model [
The generalized production and technological function (PTF) can now be represented as: () = [(, (), (), (), Φ( ), (), (), (); ⃗].
It can be used to study sustainable development.
In the general case, the integral level of sustainable development can be represented as a nonlinear function:
() = [(), (), (), (), Φ( ), (), (), (), ⃗].
Private versions of the PTF model: a) Mankiw-Romer-Weil model. Option of accounting for human capital H in the production function (PF), along with physical capital (), labor () and natural ( ) resources: () = () · () · [() · ()]1− − , where , > 0, + < 1; ; () – function of scientific and technological progress. Note that – is a part of capital provided by investment growth (capital costs); is similar. b) Model of accounting for all fixed assets:
() = () () · () · () · () · Φ () · () · (), where , , , , , , > 0 and + + + + + + = 1.
The following notations are also used here: – physical capital, – labor (labor), – human capital, – social capital, Φ – financial capital, – natural resources (land, water, etc.), () is a function of the level of scientific, technical and technological development, for example, () = (), where () – volume of innovative technologies (resources). (4) (5) (6) (7)
In [
[ ̇ ()] − () = [ ()] 1 · [ 11 ()1()] 2 · [ 1 ()()] 3 · [()] 4 + (, ) (), (8) where () – stock of knowledge and technologies in the economy – the number of inventions that have not lost their relevance by the year ; ̇ () – increase in the stock of knowledge per unit of time – the number of new inventions per year minus obsolete; 1() – the volume of skilled (more precisely – highly skilled) labor (skilled labor force with qualifications, i.e. the product of the number of skilled workers 1() and the level of qualification of the average employee ℎ(), i.e. ℎ()1()); s(t) – social index; – the rate of knowledge attrition due to its obsolescence > 0; 11 () – share of skilled labour employed in the R&D sector 0 ≤ 11 () ≤ 1; 1, 2, 3 – static parameters 0 ≤ 1 ≤ 1, 0 ≤ 2 ≤ 1, 0 ≤ 3 ≤ 1; – scale parameter: > 0. Here { (), ∈ } – white noise with continuous time; (, ) – volatility coeficient.
From [
[ ̇ ()]+ () = [ ̇ ()+ ()] 1 · [ ̇ ()+ ()] 2 [̇()+ ()] 3 [̇()+ ()] 4 (9) where ̇ () is the increase of the STP index caused by the change in the number of advanced production technologies used in production per unit of time, – the rate of decrease of the STP index due to the obsolescence of advanced production technologies, > 0; 1, 2, 3, 4 – static parameters, 0 ≤ 1 ≤ 1, 0 ≤ 2 ≤ 1, 0 ≤ 3 ≤ 1, 0 ≤ 4 ≤ 1; – scale parameter; > 0.
Note that () – STP index, dependent on the number of advanced production technologies () and used in production, for example, () = [()], where − .
Now in this generalized and integral variant we can use the conditions of development
stability from [
This construction of the indicator will reflect the importance of each of the considered components: eco-economic and socio-humanitarian subsystems (spheres) in the performance of the objective function. A change in any of the private indicators leads to a change in the value of the aggregate indicator and captures a change in the steady state of the region. In the general case, all indicators change over time, i.e. have a certain dynamic.
Simple conditions for sustainable development (SD) are defined as follows.
1) Condition of weak stability: where 2) Condition of strong stability: [· ]
≥ 0 +1[· ] ≥ [· ], [· ] = [(), (), (), (), Φ( ), (), (), (), ⃗] [· ] ≥ 0 , = + ≥ 0, +1 ≥ , = 1...4 (10) (11) (12) where – critical part of natural capital, and – natural capital, which can be replaced by artificial.
For example, given critical natural capital , sustainable development can be supplemented by a time limit on depletion of this value. For a time-decreasing production function, the arguments of which are aggregated variables: labor – , capital – and natural – resource , we will have the ratio: (, , ) ≤ +1(, , ) (13) or, in the general case:
((), (), (), (), Φ( ), (), (), (), ⃗) ≤ ≤ (( + 1), ( + 1), ( + 1), ( + 1), Φ( + 1), ( + 1), ( + 1), ( + 1), ⃗) (14) And it also requires compliance with the condition of not decreasing in time the value of , i.e. = + , as well as the condition of partial replacement of natural capital by artificial (or non-renewable resource for renewable resource): = + .
The integrated level of sustainable development for all capital (resources) can be defined, for example, in the case of linear dependence as:
() = 1() + 2() + 3() + 4 () + 5Φ( ) + 6() + 7() + 8 (), (15) where 1, 2, 3, 4, 5, 6, 7, 8 are weight (normalizing and scaling) coeficients.
This paper presents and develops a cognitive approach to modeling sustainable development of complex technogenic production systems in the innovation economy. We propose an integration model of sustainable development as a family of models for creating integrated information systems of ecological, economic and socio-humanitarian management of various social and organizational systems, especially economic objects of anthropogenic nature. We also present a cognitive model of nonlinear system dynamics that takes into account the dynamics of the humanitarian component with management in general. Furthermore, we introduce a model of innovation capital dynamics for the eco-economic and socio-humanitarian system (EESHS), as innovation capital is broader than intellectual capital by its nature and content. We derive an extended integral model of nonlinear stochastic dynamics of EESHS in the innovation space.
Our approach is based on the theoretical foundations and paradigms of systems of type “X”, integral models and the problem of sustainable development, models such as “NMSSD” and systems such as “SEEHS”, convergent technologies “NBIC” and “NBIC⊕ SG”. We show how these concepts can be applied to understand and manage the complex dynamics of technogenic production systems in the context of innovation economy.
We also demonstrate how our approach can address the challenges posed by the transition to an information society, which leads to a change in the structure of total capital in favor of human capital, an increase in intangible flows, knowledge flows, intellectual and innovative capital. We investigate the problem of sustainable development based on 8 important assets that support the sustainability and viability of EESHS.
We claim that our approach can increase the eficiency of solutions in the management of technogenic production systems, enhance the utilization of innovations and identify areas of innovation strategies for the regions.
The presented result requires further research, generalizations and computer experiments on real data. We plan to extend our approach to other types of complex systems and domains, as well as to incorporate more cognitive factors and methods into our models. We also aim to develop practical applications and tools based on our approach that can support decision-makers and stakeholders in achieving sustainable development goals. [27] V. Pankratov (Ed.), Strategy of socio-economic systems development based on foresight and cognitive modeling methodologies, Kyiv, 2017. [28] E. Gorlacheva, Metodologiia upravleniia kognitivnymi faktorami proizvodstva vysokotekhnologichnykh promyshlennykh predpriiatii, D.Sc. thesis, specialty 08.00.05, N.E. Bauman Moscow State Technical University, Moscow, 2020. [29] B. Z. Milner, Innovative Development: Economics, Intellectual Resources, and Knowledge
Management, Infra-M, Moscow, 2009. [30] V. M. Geets, V. P. Seminozhenko, Innovative prospects of Ukraine, Constanta, Kharkiv, 2006. [31] V. Halitsin, S. K. Ramazanov, Integral stochastic nonlinear model of dynamics of innovation economy, Modeling and information systems in the economy (2016) 50–64. URL: https: //ir.kneu.edu.ua/handle/2010/22805. [32] M. Z. Zgurovsky, Sustainable development in the global and regional dimensions: analysis according to 2005, Kyiv, 2006.