Fractals and chaos theory
Golden section, representing one of the most striking manifestations of natural harmony, was revealed in fractal geometry and chaotic dynamics, which are now the most modern and quickly developing sections of mathematics. The analysis showed, that dimensions of many classical fractals can be more or less precisely expressed by means of golden section. It was determined, that one of characteristic features of Mandelbrot set, which is fractal and attractor of chaotic dynamics, are numerous proportions of golden section contained within its geometrical structure; we might say, that Mandelbrot set is structured with golden section. We found out, that the beginning of dynamic chaos for all two-digit elementary functions is characterized with golden section, appearing while calculating points of bifurcation and constructing diagrams of orbits. Finally, we empirically revealed connection between two universal constants - golden section and Feigenbaum constant, which plays the most important role in chaotic dynamics [1].
Thermodynamics:
We went on analyzing one of the most important sections of theoretical physics - thermodynamics - for the purpose of searching duality and golden section in it. There were revealed two ways proportions of golden section arise in the Carnot cycle - one of the central links of thermodynamics. Besides, the generalized golden section, worked out to be used by electronic computers, was also found in the Carnot cycle. It was demonstrated, that the Carnot cycle, in a sense, is a binding link between the Carnot cycle and Feigenbaum constant: setting one of the above mentioned universal constants at the "entrance" of the Carnot cycle (i.e. in the argument of functions, describing it), we receive the other one at the "exit" of the given object (i.e. in the describing functions). Thus, a certain connection was revealed between thermodynamics and chaotic dynamics, the one, that arises due to the presence of golden section proportions in both mentioned sciences [2].
It can be seen, that golden section arises in all mentioned objects - thermodynamics, Carnot cycle, fractal geometry, and chaotic dynamics - due to the fact, that they all have a dual structure. This proves the tendency of golden section appearance in dual objects, i.e. the fact, that duality often generates golden section [1,2].
High level of transparency, liquidity, volatility and interconnection of modern financial markets (both stock and currency ones), allow to consider the very markets as global dynamic networks. The analysis, we carried out, revealed isomorphism of dynamic networks and a crystalline solid state, which allows to analyze financial markets efficiently and validly, using already worked out and applied methods of solid state physics [3].
We established a detailed mutually-simple correspondence between a crystalline solid state (described by t - J model [4] and t - J - A model [3]) and financial market. All physical notions of the above mentioned models were given a correspondent economic interpretation, oriented to analysis of the financial market.
Using the established isomorphism of financial market dynamic networks and a crystalline solid state, we successfully applied theoretical methods of solid state physics (in the frame of t - J model and t - J - A model) to analyze financial markets (both stock and currency ones), namely:
In the frame of Hubbard model at arbitrary coulomb interaction and electron concentration, we calculated two boson Green functions, which describe distribution of collective excitations of the electron system - magnons (states with one electron spin turned over) and doubloons (states with two electrons placed on one junction of a crystalline lattice).We revealed a similar external structure of a madnon and doubloon Green functions and found deep internal resemblance between these functions. By means of magnon Green function we analyzed instability of paramagnetic phase relatively to appearance of spin regulating. Due to doubloon Green function there was analyzed instability of metal phase relatively to appearance of charge regulating. We received criteria of phase transitions "paramagnetic-ferromagnetic" and "metal-dielectric".
1. Conceptual substantiation of stages of the Russian bank system development under transition to decentralized economy of market type, predetermined by changes in the structure of system limitations and contradictions in the process of credit system evolution. The offered classification of stages to system contradictions and limitations distinguishes three groups of factors, namely:
They played a decisive role in formation of structural and institutional peculiarities of the bank sector development. System tensions resulted in the fact, that second level of the bank system turned to be divided into 5 different groups of banks:
The process of differentiation, complication of the bank structure, inevitable transition to a new stage of system formation prove evolutionary character of changes in the bank sphere.
2. Opening of regional banks functions in accordance with the offered conception as elements (units) of national settlement and credit network, set as close as possible to the centers of material production, and playing an important role in providing national economic security. In this connection there should be taken state measures on preserving and developing regional banks, reducing system risks, which arise due to over-concentration of capital in a not numerous group of Federal banks.
3. Evidences of a broad structure of the bank system, consisting of state, private, (mixed) banks and non-bank organizations in the process of further evolution of the complex system of redistributing financial resources on the way of mutual supplementing and preserving dynamic equilibrium between various elements of the system, intensifying the role of various forms of financial self-organization of the population: credit unions, loan-and-savings and construction-and-savings banks and others.
4. Invention in practical and scientific vocabulary of a notion of "unequal competition", as a specific kind of competitive advantages, enjoyed by banks, using financial resources of the State, subjects of Federation, municipal institutions in the form of various budget and non-budget funds, and resources of unitary state enterprises in case, if they directly forward them to replenish banks' capitals. This deforms the market environment, limits potential development of banks due to suppression of competition, generates conditions for corruption.
5. Defining concretely six conceptual principles of the bank system development in the country, their wide application as terms for self-organization and self-development. They are broad structure, equal competition, market discipline, priority of national interests, financial and economic federalism, flexible regulation. Each of them opens a certain channel for the system progressing, while they all together form a conceptual frame, which should serve as a basis for elaborating laws, resolutions and normative acts, preserving evolutionary trend of bank development.
6. Evidences of high importance of the following factors, while considering approaches to evolutionary conceptions of management:
7. Application of models, using analogy of competing agents conduct under limited resources in ecosystems and banks interaction, allow to receive a number of highly important results:
8. Confirmation, with the help of the method of pattern recognition, of logical and comparative analyses conclusions on presence of five typical classes of banks within the second level of the bank system, and generalization, that division of banks on groups sufficiently reflects the real hierarchy of the bank system on the resource scale and corresponds the idea about self-similarity of markets (scaled structure of interacting market sectors).
9. Determination of crisis as a dual process of formation and destruction of connections between elements of the organizational complex, which results in break and restoration of equilibrium. This allowed to ground a qualitative model to analyze banks stability ("pyramid of problems"), assuming a qualitative generalization, and make an important theoretical and practical conclusion, that anti-crisis management represents purposeful influence through the change of the organizational form of an anti-crisis management object by either introducing or (and) breaking connections.
10. We received a general, basic, and modification conceptual models of competition in economic systems.
11. We systematized well-known description of some stages of competition life cycle, related to various fields of knowledge. Then we received a base model of competition life cycle, including three different stages of functioning and, correspondingly, two transitive stages of development/reengineering, separating them.
12. We mathematically grounded interconnection of the phase portrait of an economic agent/a system and empirical triangle diagram of Graim. There was shown a correspondence of well-known competitive strategies of economic agents (ruderal, competitive, stress-tolerant) to various sections of trajectory, which allowed to systematize competition life cycle in economic systems and quantitatively classify competitive strategies of agents on empirical data. We also demonstrated the influence of external computer conditions on the choice of an optimal competitive strategy, the agent makes. The Institute calculated phase portraits of various life cycles, differing from the classical one.
13. There was formulated a hypothesis about possible synthesis of existing mutually excluding competitive theories (perfect, imperfect, and monopolist competition) based on ideas about competition life cycle.
Identification and classification of objects by methods of pattern recognition
An article by G.D.Gloveli "Productive Forces As Paradigm Category of Russian School of Economic Thought" opened the rubric "Historical politeconomy" in "Herald of the International A.Bogdsnov Institute". This rubric intends to publish investigations, developing the principle of historism in political economy, applied by A.Bogdanov in his courses of political economy
G.D.Glovely wrote the bigger part of the section "Economy through centuries and countries", including the topic about A.A.Bogdanov and tectology for the tom "Economics and Society" of the Children's encyclopedia "Avanta Plus"(which is to be released in 2002) and 4 articles for the rubric "Entertaining History of Economics" in "School Economic Journal". This rubric is considered as approbation of the future book by G.D.Glovely "Entertaining Economic History", popularizing A.Bogdanov's contribution in political economy.
On analysis of golden section and duality:
On analysis of competition:
In press: Popkov V.V., Berg D.B., Kapralov M.V. Quantitative classification of Russian banks' competitive strategies / Banks and technologies.
On the analysis in the field of Solid state physics:
Theses of conferences: