INTEGRATING MODEL FOR SUSTAINABLE DEVELOPMENT

ISSN 1681-6277. Economics and Law. 2019, No 4 (55): 124—139 © S.K. RAMAZANOV, I.V. ZABLODSKA, D.V. ZABLODSKA, 2019 The article presents the integration model of sustainable development as a family of models for creation of integrated information systems of ecological economic and socio-humanitarian management of different socio-organizational systems and especially economic objects of technogenic character for ensuring the sustainable and viable development. The problem of sustainable development for the "hexagon" of main assets (capitals), supporting the vital activity of socio-ecological-economic systems is considered and defined: the concept of sustainable development, the system of sustainable development global dimensions, and the level of sustainable development.

Integrating model for sustainable development be based not only on a rational-intellectual approach to the consideration of ecosystem, but also to rely on its spiritual and cultural components. If the mechanism of activity optimization while moving to the noosphere is the mind, then spiritual and moral criteria are evaluative characteristics of it, since spirituality is opposite to the material and natural factor and not rational or irrational [1,4,11].
At the same time, the most important problem is the integration of science, education and technology based on the noosphere paradigm of sustainable development.
Why do we need integration? In the whole humanity history, the history of Eurasian space countries, there were many different crises, conflicts, wars, cataclysms that threatened the existence of life on Earth. However, each time, humanity found the strength to unite intellectual, material and spiritual capabilities, which ensured the preservation and development of life on Earth in all sorts of evocations. Today the world is once again in a global crisis, and the integration of opportunities is again required.
Why, above all, the integration of science, education and technology is necessary? Because of this integration, we get an answer to the question "How?" to preserve the development of humanity in the conditions of diverse and multidimensional external (space), internal and hybrid threats. The answer to the question "How?" will presupposes the existence of a developed system of measurement (measures) combining science, education and technology. The fundamental rules for in te grating the values of science, education and technology are: a) harmonization: science -educa tiontechnologies are integrated and form a com plete system, if proportionality of their basic principles and laws is ensured by eliminating gaps in dimension; b) innovation; c) fundamental nature: the use of fundamental knowledge and the results of the noosphere paradigm of sustainable development.
All world scientific schools have the aim to preserve Earth for the future generations. However, to achieve this goal, they offer different methods. For example, the western school offered the control of population growth (the strategy of the "golden billion"), the eastern school offered the observance of dogmas (the strategy of Eternal life), and the Russian school offered the transition to the noosphere, i.e. strategy of noosphere sustainable development.
An innovative model of sustainable and safety development of societies and the world as a whole should be built because of an integral paradigm of socio-ecological-economic unity and socio-humanitarian technologies. The following system as "Creator -Man -Socio-humanitarian-ecological-economic environment" is the object for system analysis studying, synthesis, innovative technologies of modeling and management. At the same time, a global goal to ensure the safe existence and sustainable development of the entire world civilization is the research and development of integral models of the entire system with the following orientation structure (Fig. 1).
Here SHS -Socio -humanitarian system; PSpolitical system; IT/S -innovative technologies and synthesis; R(t) -input effects on the sys tem (resources, specified regulatory functions, conditions, time and other restrictions); Y(t) is the integral output of the system(both "useful" and "harmful").
The concept of sustainable and safety development implies a change of the traditional economy paradigms, the humanization and ecologization of its main principles, the search for common approaches and the consistency of concepts for the development of ecological and socio-economic systems. During recent years, a new interdisciplinary field of applied science has emerged it is an ecological economics. Ecological economics is a new field of research that deals with the relationship between natural ecosystems and socioeconomic systems in the broadest sense, relationships that are crucial for many current problems of humanity, as well as for building a sustainable and high-quality future.
Therefore, in the current conditions of instability and crises, the problem of developing me thods S.K. RAMAZANOV, I.V. ZABLODSKA, D.V. ZABLODSKA and technologies of analysis, modeling, forecasting and decision-making for the sustainable development of viable socio and economic systems becomes even more urgent. These systems are characterized by complexity of structure and behavior, synergetics, nonlinearity, and have other "NO" and "MANY" characteristics factor and features [1,4].
Moreover, a very important problem is also the study of systems with integral properties, that is, systems that include socio and ecological economics and humanitarian subsystems (SEEGS) as systems of the future (noosphere type systems) in their structure. Local regional production systems such as technogenic industrial systems (TIS) are also SEEGS type systems.
Traditionally the methods and models of management and decision-making that are based on the object approach are traditionally used to investigate and solve these problems. Recently, however, a number of scientific publications and scientific schools have emerged, focusing on the importance and necessity of accounting for the dynamics of the subject's behavior, the use of a subject-oriented and reflexive approach [10,11].
This article proposes the models and technologies for managing the viable and sustainable development of the TPP of the region as a SEEGStype system based on an integrated object and subject oriented approach. The conceptual model, a generalized synergistic model of dynamics with uncertainty (stochastic and chaotic factors), as well as a variant of a nonlinear dynamic model of subject behavior of management and decisionmaking, the decision-maker person (DMP), etc., are offered.
In the conditions of future transition of society to the sixth, and especially to the seventh technological ways of development, when creating the integral models and technologies, it is essential and important to take into account the socio-humanitarian fact, reflective and subject-oriented approaches, etc.
The purpose of article is the following: to show the importance and necessity of ecological economics and socio-humanitarian micro and macro models development integral that based on the mo dern theories and analysis problems of modeling, forecasting and management of ecological economics, social-humanitarian systems and technologies, taking into account the instabilities to ensure safety and sustainable functioning and development, to offer some concrete results.

Material of the main results.
An overview and analysis of some obtained results in recent years by various authors on macro and micro modeling of dynamics of ecological economics and sociohumanitarian systems and processes that function and develop in complex conditions of nonlinearities, instabilities and crises are proposed. A brief description of the results with the necessary sources for detailed reading was provided [1][2][3][4][5][6][7][8][9][10][11][12][13][14]. The author hopes that this material will be useful for well-known specialists of researchers in this field of science, and for young scientists also.
1. The conceptual model of integral ecological economics, socially-humanitarian development and management of a complex system in the conditions of uncertainty, instability, complexity and the like "NO-factors" and "MANY-factors" can be represented in the form of a theoretical-multiple tuple of the form [1,4,11]: T   I I I I  I  I   I I I   :  , , ,  ; , , , , where c n o u E E S , , ,Η 〉 -integral tuple of the basic set of systems, moreover c E -economy (economic system); n E -environment (eco-sphere); o S -social sphere (social system); H u -humanitarian components in the model. The tuple consists of well-known components for each of the above systems.  I  I I , , , , ... -a tuple of resources, R c and R n -economic and environmental resources; I n -investments; τ II -information and innovation potentials; R S -a resource to ensure security against a range of threats, risks and crises.
The general scheme of sustainable and sociohumanitarian development integral model of global (world) system, which the authors call the noosphere model of development, can be represented as an integrator: S = E n ⊕ E c ⊕ S o ⊕ H u -an integral "4-unit" system in which the subsystems: E c -economic system, E n -ecological system, S o -social system, H u -humanitarian system; X(t, r) -state of the integral system S; in the space of variables (t, r) ∈ [T × R 3 ]; X 0 -state of the system S at the initial moment of time t 0 ; Wset of disturbing environmental factors.
-3.4 and 1.4-3.4 and others, require further examination, analysis and determination (Fig. 2). Thus, the system (model) of sustainable development is the integration of 1 + 2 + 3, and the NMSD can be called as the noosphere model of sustainable development ("civilization model") and defined as a set ( , which defines a system with integral properties. 2. The conceptual model of forecasting and control of ecological economics processes (EEP) of technogenic object in the conditions of "NO" and "MANY" factors existence can be represented in the form of a theoretical-multiple model as a tuple: , , where X -the set of possible states of technogenic economic object (TEO); Y = 〈Y ecn , Y ecl 〉total output of technogenic economics object, and Y ekn -a productive set (useful output), and Y ekl -a set of pollution (harmful output); F = = 〈F ecn , F ecl 〉 -a model display of feasibility stu dy; H = 〈H ecn , H ecl 〉general observation ope rator (mea surements); R -resource set ( the main controlled input of feasibility study); E -the set of indeterminate factors (both external and in ternal, both additive and multiplicative), in particular, this is a set of stochastic, fuzzy, multiple or mixed nondefinitions; Ω -many restrictions; T -time interval of feasibility and development of feasibili ty TEO study; G -target set; K u -a generalized ecological and economic management criterion (ECE); K p -generalized criterion for forecasting optimization (CFO); P -ecological and eco no mic forecasting operator (predictor); U = 〈U ecn , U ecl 〉vector of ecologic and economic mana gement (EEM). The terms "ecn" and "ecl " corres pond to economic and environmental variables.
The aim of optimal ecological and economic forecasting, predictor definition, both for internal and external processes, can be formulated as follows: to determine the estimation of x(t k + δ), δ = δ 0 , δ 1 ,… state vector x(t k + δ)at a predetermined forecast step on the basis of multiple ecolo gical and eco-nomic observations {y(t), t ∈ [t 0 , t k ]} and according to a given CPC K p .
The task of EES is to determine the effective integral control vector U = 〈U ecn , U ecl 〉 based on estimates x(t k + δ), δ = δ 0 , δ 1 ,… and a nonlinear dynamic ecological and economic model of TEO that achieves G under the given generalized ecological and economic criteria K u and constraints Ω , taking into account uncertainty and risk conditions.
The multiplicative additive stochastic model with the chaotic dynamics in the general form can be represented as vector equations: or, a multiplicative additive stochastic model with the chaotic dynamics and control, i.e. subject to the impact management: The observation model is represented: The following notation is used here: t t (( ), ( ), ξ ζ t ( ) η -multiplication additive stochastic components in models (2)-(4), λ(t) -chaotic compo-  (2). The remaining notations are given above.
3. The integral socio-ecological economics dynamic model of behavior with spiritual and moral variables can be conceptually represented, in the general (in block) form: is the combined vector of behavioral variables and states of socio-ecological economics system, taking into account the variable level of spirituality (SEESD) -X 4 , and in (5) X 1 = X 1 (t) -the vector of economic variables; X 2 = X 2 (t)-the vector of environmental variables (pollution variables); X 3 = X 3 (t) -the vector of social variables; P = (P 1 , P 2 , P 3 , P 4 ) -the cumulative vector of SEESD parameters (internal and external environment); ( ) 1 2 3 4 , , , Ξ = ξ ξ ξ ξ -the vector of external random and indefinite variables. For example, for TPS [1,11] ( ) -the vector of some parameters of consumption (costs), and C 1 -the value of social consumption (wages, etc.), C 2 = C e -consumption for the environment, C 3 = C s -consumption for safety, C 4 = C i -volume of investments for innovative, information and humanitarian technologies.
A generalized diagram of an integrated hierarchical object-and subject-oriented control system and DM is presented in Fig. 3.
Subject-oriented management and decisionmak ing (SOM and DM) in Fig. 3 is presented in the block "Control subject and DM", where k, e, r are the corresponding modes, k-cognitive variables, e-emotional-psychological variables, r-reflexi ve variables, which together determine the dynamics of persons behavior who is a decision maker.
4. A synergistic model of nonlinear dynamics of integral stochastic system with the chaotic behavior in a generalized form can be represented as: where 〈ξ i , w i 〉 are the stochastic perturbing components of model; {a ij (t)} -non-stationary components of model; {d ij } -diffusion coefficients that determine the level of state variables distribution; Σ X -total maximum (maximum allowable) value of vector X; {λ i } -a set of parameters that lead to randomness.
In particular, this model can also be represented as a system of equations: where X i -coordinates of the system state vector, and  Such models describe and encompass a broad class of complex processes and systems to which NMSD relate.
5. Modeling of ecological and economics dynamics of development management of technogenic system in the conditions of uncertainties and risks (variants of general formulation). The problem of technogenic economic system control (TES) as a super-complex dynamic nonlinear system with the aim of translating it into a state of socially and ecologically oriented economic system (SSEOES) is urgent [1,4].
.., ( )) -a phase vector of macroeconomic (or socio-economic) variables (parameters) that describes the state of economic system at time t. The changing in the vector time x(t) satisfies the nonlinear differential equation (synergistic equation): .., ( )) -control vector (decision-making elements) whose coordinates characterize the mode of economic activity at time t; = .., ( )) -the vector of external disturbing factors, the elements of which characterize various accidental and indefinite influences of external environment (or the effects of negative side); it may be, in particular, the vector of interference; t 0 -the initial moment of time; ) of equation (6) determines the trajectory of development from TES to SSEOES. In this case, it is assumed that the control vectors and the interference vector satisfy the given constraints: where is defined by the economic laws and / or balance ratios and corresponds to the real economy.
So, it is necessary to define the control vector (vector of economic decisions) that provides the "optimal" in some given sense the movement (development) from TPP to SSEOES and satisfies the set requirements that can be formalized in the form of conditions: where X T -the phase space of admissible(desirable) states of SSEOES; X S -safe transition area; T = φ (x (·)) -the moment of falling into the desired state (i.e. moment of first hits x (t) in a great number T X ). We note that here the problem is solved under conditions of uncertainty over the vector v (t) and either programmatically (which is not entirely acceptable for modern economic systems) in the form of a definition of control ⋅ = ≥ u u t t t 0 ( ) ( ( ), ) at the initial moment t 0 as a fixed function of time defined over the entire subsequent time interval, or by the inverse principle communication (and adaptively according to information), when the control is formed during the transition depending on the incoming information and new knowledge, for example, in the form u (x (t)).
Assuming that in the process of transition from TES to SSEOES, it is possible to measure (obtain) observations of only some part of the components of x t ( ) vector, for example, the first < m n ( ) components (i.e, a vector = m m X t x t x t 1 ( ) ( ( ), ..., ( )). Then the control u (t) is defined as a function of X m (t), from the incoming information: where u (t)∈U the definition of a function F is a control strategy and a F ∈ ℑ set of valid strategies.
Thus, the task of transition (development) managing is to construct a strategy F 0 that guarantees the fulfillment of the following conditions: for the interference vector v (t)∈V and the initial state x X 0 0 ∈ for the trajectory ⋅ = ≥ x x t t t 0 ( ) ( ( ), ) of controlled TES transition which is described by the equation: The conditions (7) must be observed. Let be ℵ[X 0 , F ] -the set of transition trajectories x (·) of system: which is obtained by sorting through all the starting points x X 0 0 ∈ and all permissible interference ). Denote as ℵ -the set of all continuous functions x(·) for each of which the conditions are fulfilled: • there is a time T = φ (x (·)), the first time x (t) ∈ X T ; • condition of risk-free transition (development) is satisfied, fulfillment of the condition x (t) ∈ X S in interval t 0 ≤ t ≤ T (x(·)). S.K. RAMAZANOV, I.V. ZABLODSKA, D.V. ZABLODSKA Thus, considering the task of controlling the phase transition (development) can be reformulated as follows: in the class of admissible strategies, it is required to define a strategy F 0 ∈ ℑ , for which the condition is true ℵ ⊂ℵ . To formulate one of variants of this problem, let us introduce some functional of effective control given on the development paths of system, i.e. the quality of strategy F 0 is evaluated by the value of the functional J that it takes on the most unfavorable trajectory from the beam ℵ[Ω 0 , F ], where t X 0 0 0 Ω = × is the initial development space. Now we can formulate a particular problem of strategy optimization.
It is required to determine a strategy F, that satisfies the condition: [ , ] min sup [ ()].
If the optimum of functional J [x(·)]is not achieved then for an arbitrarily small one ε > 0, a strategy F ε can be defined such that: This setting can be called a game, in which the choice of F is the strategy of the 1 st player, and the choice is the strategy of the 2 nd player. Game and optimal methods for solving this problem have been developed by many domestic and foreign scientists [1]. 6. A variant of the socio-ecological and eco nomics model of dynamics and a technogenic industrial enterprise / region (TIE / TR) [15][16][17][18][19]: where Y -the volume of "useful" output, K -a capital, L -the number of workers (labor), Cthe volume of consumption, Z -the amount of pollution ("harmful" output), I -the investments, R -other resources, D -expenditure to monitor and reduce pollution. Then the three points in this model determines the environmental and economic strategy for the development of TIE / TR, and a u = (C, Y, Z) is the vector (strategy) of environmental and economic management.
7. Modeling of ecological economics optimal management of the TIE / TR [1]. 7.1. A variant of ecological and economic model of the TIE. Since the increment (growth) of pollution is equal to the difference between the volume of pollution produced and the volume of pollution eliminated due to direct control, as well as a result of natural decrease (assimilation), the dynamics of pollution in general can be described by the following differential equation: where for the TIE ( ) and for the regional economy as a whole, in particular for the technogenic region (in the case of mutual independence of the TIE): Suppose that a rate of accumulation ( ) t ρ = α = α is a variable. Then the specific consumption can be calculated as: In this case, the equation of funds dynamics will take the form: At the same time, it should be noted that the investment flow is also a stochastic process.
Equation (12) is the main dynamic model of a controlled production system (PS) and as a control variable, we can take the specific consumption = с t С t L t ( ) ( ) ( ) or rate of accumulation ρ, and the state variable k(t) -is the capital-labor ratio, i.e. = k t K t L t ( ) ( ) ( ). 7.3. Nonlinear modified dynamic model of the production system with the logistic nature of the change L. Traditionally, an exponential change in labor resources is assumed, i.e. . However, taking into account the effect of "saturation" there is a more realistic model of the dynamics of labor resources in the form of logistic equation: where L max -the maximum allowable amount of labor resources (the maximum allowable number of employees in this system). Therefore, we will have the following model of functioning and development of the TIE: For the convenience of syem analyzing, we turn to relative (specific) values: k K L / = -ca pitallabor ratio; c C L / = -consumption per wor ker; y Y L / = -labor productivity. Then the system of equations (13) can be rewritten in the following form: Thus, we have a nonlinear dynamic model: Since the dynamics model of labor resources has the form: So, for the TIE, as an integral ecological and economic model of dynamics, we can consider equations (11) or (12) with a state vector = x k z ( , ) and a control vector of variables = α β u ( , ). The task of optimal control of the TIE can be presented in the following statement.
Let we take as a utility function ≡ U q ( ) ≡ α β ≡ U k z U x u ( , , , ) ( , ) , and the efficiency (optimality) functional - Then the problem of the optimal EED will take the form: Under the restrictions: ≤ α β ≤ α + β ≤ 0 , 1, 1}, also 8. The cyclic dynamics models and a generalized logistic equation to describe the sustainable development processes and technologies. The process of each technology development in the most general, approximate form is described by a logistic curve determined by a differential equation of form [25]: Where t -is a parameter that expressing the total costs of society for the development of this technology (it can be time, energy or abstract social labor, expressed in cost form), y(t) -is the technologically significant result achieved by this technology, αis a positive constant ("scale" parameter), k 1 and k 2 -are positive constants that limit (technically lower and upper) the technolo-gically significant result of this technology functioning. Moreover, k 1 -is the lower boundary y(t), which expresses the initial, starting, and extremely low capabilities of the technology, and k 2 -is its technological limit characterizing its maximum capabilities.
With an increase in the costs of mastering and improving this technology, its technologically significant result can only increase; therefore, y(t) is a function that grows monotonously throughout the entire area of its definition. The fact that the first derivative (growth rate) of y, according to equation (15), is directly proportional to the separation of this quantity from its starting capabilities, means that y(t) grows faster, the larger this separation. On the other hand, the proportionality of the first derivative to the value (k 2 -y) means a slowdown in the growth of y(t) as it approaches to its technological limit.
The logistic (S-shaped) curve describing the life cycle of each individual technology (Fig. 4) can be considered as a model of the dynamics of various cumulative quantities, so that the rate of further growth of such quantities is proportional to their existing value.
Logistic curves describe the cumulative growth with saturation; meaning that accumulating value has an upper limit, as it approaches its growth slows down.
With such cumulatively growing quantities that not only the dynamics of individual technologies are described, but also the scientific and technological development of society as a whole. For example, N.D. Kondratiev noted [24] that the level of technology as a quantity allows quantitative measurement and exerts a quantitatively measurable effect on the elements of economic life is a cumulative quantity whose dynamics obeys a law expressed by a differential equation of the form (15).
From time to time in society, the process of replacing technologies is performed, i.e. the change in the prevailing technology, in accordance with which the bulk of the entire mass of given use value, a given product of human labor, is produced. The displacement of technology from production processes and its replacement with a more progressive one is called a technological leap. The process of replacing technologies, the dynamics of each is expressed by a logistic curve.
For the practical calculations the period of technological gap can be considered, as shown in the figure, the time between the closest points of lo cal maximum curvature of two adjacent logistic curves (that is, between the points closest to each other, where these adjacent curves are most "convex"). Fig. 4 have more general meaning than the illustrations to the development process of individual technologies or to the life cycles of innovations Overall, the development of productive forces of society (both locally and globally) appears as a cumulative process, the dynamics of which obey the logistic law.
In the modern world economy the duration of industrial cycles is reduced, and the most significant are becoming the long waves of economic conditions, which are the information cycles (Kondratiev's cycles), the dynamics of which are based on the universal laws of aggregate social knowledge development and are associated with the life cycles of corresponding technological structures.
These information cycles the duration of each is 50-60 years, also do not cancel either agrarian or industrial cycles, exist along with them, but gradually acquire a decisive, dominant influence on the nature of economic dynamics, on the course of macroeconomic processes.
The current stage of economic development gives reason to say that medium-term cyclical factors are increasingly fading into the background compared with the factors of a structural long-term nature, that the classical cycle is being formed within the framework of a large cycle of economic conditions. This fact, generally speaking, means that in modern conditions, the long-term economic interests have priority, dominant nature compared with short-term, current ones, and the assessment of the long-term consequences of decisions taken is of primary importance.
The life cycle of each technological structure lasts on average about 100 years.
The first of them falls at the beginning of the technological mode development due to technological, internal reasons caused by the laws of new tech nologies proposals, when this structure makes its way into an alien socio-economic environment.
The second rise is at the beginning of the second half of its life cycle, when economic relations in society have already transformed sufficiently to absorb the technological innovations offered by this structure. This rise was caused not by the technological, but economic reasons, external to the development of the technological basis of production, and expresses the readiness of society for the implementation of relevant innovations and a regular increase in public demand for them. Note that these two impulses in the development of technological structures -endogenous and exogenous -generally express the quantitative dynamics of various progressive-cyclic processes; the refore, this model can serve to describe many similar phenomena in nature and society. In re lation to the quantitative dynamics of technological structures, this model is called as the hypo the sis of Grubler-Fetisov and allows to predict with sufficient accuracy the onset of transitional and crisis periods in the development of technical and economic macro-systems and individual technologies.
In general, the replacement of technological structures is carried out according to the law, which is mathematically described by a generalized lo gis tic curve. This function satisfies the differential equation for fixed constants k 1 and k 2 (k 2 > k 1 > 0), which express the technological limits characteristic of a given technological structure, so that for all t: k 1 <y (t) < k 2 : = α − − dy t y k k y dt 1 2 ( )( )( ).

The solution of this equation is the function
for arbitrary b > 0, where In the model under consideration, time does not flow linearly, but in a sense is proportional to the function t ( ) α . Therefore, the form of the function y (t) essentially depends on the function t ( ) α . The simplest case t ( ) α = const leads to the Fischer -Pry technological shift model, which was first considered by N.D. Kondratiev in 1934. Less the function t ( ) α resembles a constant, the events more non-linearly described by this model are developing.
In some cases, pulse type function should be considered as t ( ) α its peak at a certain moment in time t 1 > t 0 . For example, a function of the form α =α − +γ t t t * ( ) /[( ) ] where α, γ > 0, agrees well with the hypothesis of a "double" wave of technological structures replacement. In this model, the first time rise is due to the logistic nature of the functions growth of type (16), that is, it has an endogenous nature, and the second is caused by local "compression" of time at time t 1 , that is, it is determined by exogenous reasons.
A generalized logistic curve with an arbitrary number of inflection points can be considered as a model of the learning processes of complex dynamic systems [25], in which periods of evolutionary, gradual and revolutionary, spasmodic development alternate. In this case, wave-like oscillations are superimposed on the translational trend, so that in general the development of such systems appears as a translational-cyclic process.
9. The issue of sustainable development and the "heptagon" of the main assets (capitals) supported by the vital activity of the SEES [26,27] (Fig. 5).
The generalized production and technological function (PTF) can be represented as: , , , , , ; ]. It can be used to study sustainable development.
The concept of sustainable development. Theory and practice testify that at the turn of the century the teachings of V.I. Vernadsky on the noosphere proved to be a necessary platform for developing a triune concept for sustainable environmental, social and economic development. A generalization of this concept was done at the UN world summits in 1992 and 2002, in which more than 180 countries of the World, many international organizations and leading scientists took part. Thus, the new concept systematically united the three main components of sustainable development of society: economic, environmental and social.
The economic approach consists in the optimal use of limited resources and the use of environmental, energy, and material-saving technologies to create a total income stream that would ensure at least the preservation (not reduction) of the total capital (physical, natural or human), using which this comprehensive income is created. At the same time, the transition to an information society leads to a change in the structure of total capital in favor of human capital, consolidating the intangible flows of finance, information, and intellectual property. Already, these flows exceed the volume of tangible goods movement by 7 times [ru.wikipedia.org].
The development of a new, "weightless" economy (knowledge economy) is stimulated not only by a shortage of natural resources, but also by an increase in the volume of information and knowle d ge acquiring the significance of the requested product.
From an environmental point of view, sustainable development should ensure the integrity of biological and physical natural systems, their viability, and the global stability of the entire bio sphere depends on this. Of particular importance is the ability of such systems to self-renew and adapt to various changes, instead of being preserved in a certain static state or degradation and loss of biological diversity.
The social component is oriented towards human development, maintaining the stability of social and cultural systems, and reducing the number of conflicts in society. A person should not become an object, but a subject of development.

Fig. 5. Assets of capital
Integrating model for sustainable development Person must take part in the processes of the formation of life, adoption and implementation of decisions, control over their implementation. Equitable distribution of benefits between people (reduction of the so-called GINI index), pluralism of opinions and tolerance in relations between them, preservation of cultural capital and its diversity, especially the heritage of non-dominant cultures, are important for ensuring these conditions. Systematic coordination and balancing of these three components is a task of enormous complexity. In particular, the interconnection of social and environmental components leads to the need to preserve the same rights of present and future generations to use the natural resources. The interaction of social and economic components requires the achievement of justice in the distribution of wealth between people and the provision of targeted assistance to the poor. Finally, the interconnection of environmental and economic components requires a valuation of technogenic environmental impacts. The solution of these problems is the main challenge of today for national governments, authoritative international organizations and all progressive people in the world.
The system of global dimensions of sustainable development. An important problem on the way of implementing the concept of sustainable development is the formation of a measurement system (indices and indicators) for quantitative and qualitative assessment of this very complex process. The main requirements for this measurement system are its informational "completeness" and the adequacy of the presentation of an interconnected triad of sustainable development components. Both well-known international organizations and numerous research teams are working in this direction, but so far, they have not been able to reach an unambiguous agreement on this measurement system.
Institute for Applied System Analysis Minisry of Education and Science of Ukraine and the National Academy of Sciences of Ukraine has proposed a specific system for measurement of sustainable development [26,27].
We will evaluate the level of sustainable de velopment (LSD) with the help of corresponding index, which is calculated as the sum of the indices for four dimensions (areas): Economic ( эко I ), Environmental ( экл I ), Social ( сои I ) and Hu manitarian ( гум I ) with corresponding weighting factors, t.e. I УР = α 1 I ecn + α 2 I ekl + α 3 I soc + α 4 I hum , In turn, each of the indices I ecn , I ekl , I soc , I hum will be calculated using well-known international indices and indicators.
The conditions for sustainable development (SD) are defined as follows.
2. The condition of strong stability: where N C -is a c0ritical part of natural capital, and N S -is natural capital, which can be replaced with artificial. For example, taking into account the critical natural capital N C , sustainable development can be supplemented by a restriction on the exhaustion of this quantity in time. For a production function that does not decrease in time, the arguments of which are aggregated variables: labor -L, capital -K and natural resource -N, will have the ratio:

F K t L t H t N t t S t I t c
and it is also necessary to observe the condition of nondecreasing in time the value of N с , that is