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Volume 15
Issue 1
Online publication date 2019-02-06
Title Estimation of the world economic system stability from 1963 to 2013 by using a discrete dynamic model
Author Anatoly Kilyachkov, Larisa Chaldaeva, Nikolay Kilyachkov
Authors estimated the world economic system stability, using a discrete dynamic model (DDM). DDM allows to describe the state of the world economy (whether it is stable, potentially stable or unstable) at different time intervals by means of a generalized image, a "pictogram". These pictograms are radii of convergence (Julia sets) of DDM approximating polynomials. We used this methodology to analyze the state of the world economic system in the interval from 1963 to 2013. In order to determine the type of stability of the world economy in each year during this period, we solved the following interrelated tasks: determined the coefficients of the approximating polynomials, corresponding to different years; found basins of attraction of these polynomials for different values of the coefficients; determined the patterns of convergence of the basins of attraction thus found; built the Julia sets (the radii of convergence) corresponding to them. The obtained results confirm the conclusion that the development of the world economy is largely unstable. But the stability of the world economic system has increased over the period under review (1963-2013). Moreover, the last world economic crisis was not accompanied by a loss of stability. Based on the obtained results, we conclude that the potential stability of the development of the world economic system and economic crises are not unambiguously related concepts. It is necessary to distinguish between the situations of stable development of the economy and the crisis in the economy.
Allais, M. (1977). Theories of general economic equilibrium and maximum efficiency. In Equilibrium and disequilibrium in economic theory. D. (pp. 129-201). Dordrecht: Reidel Publishing Company.

Arnold, V. (2009). Teoriya katastrof  [Theory of catastrophes]. Moscow: Editorial URSS. [in Russian].

Arrow, K. J. (1963). Uncertainty and the welfare economics of medical care. American Economic Review, 53(5), 941-973.

Arrowsmith, D. K., Place, C. M. (1982). Ordinary differential equations. A qualitative approach with applications. London, New York, Westfield College University of London: Chapman and Hall.

Bezruchko, B., Koronovskiy, A., Trubetskov, D., & Khramov, A. (2010). Put' v sinergetiku [The way to synergetics]. Moscow: Book House "LIBROKOM". [in Russian].

Blaug, M. (1985). Economic theory in retrospect (4th ed.). Cambridge, NY, Port Chester, Melbourne, Sydney: Cambridge University Press.

Chaldaeva, L., & Kilyachkov, A. (2012). Unifitsirovannyy podkhod k opisaniyu prirody ekonomicheskikh tsiklov [Unified approach to describing the nature of economic cycles]. Finansy i Kredit [Finance and Credit], 45(525), 2-8. [in Russian].

Chaldayeva, L., & Kilyachkov, A. (2014). Model' obratnoy svyazi i yeyo ispol'zovaniye dlya opisaniya dinamiki ekonomicheskogo razvitiya [Feedback model and its use to describe the dynamics of economic development]. Finansy i Kredit [Finance and Credit], 31(607), 2-8. [in Russian].

Danilov, Y. (2010). Lektsii po nelineynoy dinamike. elementarnoye vvedeniye [Lectures on nonlinear dynamics. An elementary introduction]. Moscow: Book House "LIBROKOM". [in Russian].

Debreu, G. (1952). A social equilibrium existence theorem. Proceedings of the National Academy of Sciences, 38(10), 886-893. 

Debreu, G. (1962). New concepts and techniques for equilibrium analysis. International Economic Review, 3, 257-273. 

Debreu, G. (1970). Economies with a finite set of equilibria. Econometrica, 38(3), 387-392. 

Friedman, M. (1968). The role of monetary policy. American Economic Review, 58(1), 1-17.

Haken, H. (1978). Synergetics. Introduction and advanced topics. Part I. An introduction. Nonequilibrium phase transitions and self-organization in physics, chemistry and biology. Berlin - Heidelberg-New York: Springer-Verlag.

Haken, H. (2004). Synergetics. Introduction and advanced topics. Part II. Advanced topics. Instability hierarchies of self-organizing systems and devices. Berlin - Heidelberg-New York: Springer-Verlag.

Harsanyi, J. C., & Selten, R. (1988). A general theory of equilibrium selection in games. Cambridge: MIT Press.

Juglar, C. (1862). Des crises commerciales et de leur retour periodique en France, en angleterre et aux etats-unis. Paris: Guillaumin. Retrieved August 04, 2012, from

Kantorovich, L. V. (1939). Matematicheskiye metody organizatsii i planirovaniya proizvodstva [Mathematical methods of organization and production planning]. Leningrad: Publishing House of Leningrad State University. [in Russian]. 

Kilyachkov, A., & Chaldaeva, L. (2013). Bifurcation model of economic cycles. North American Academic Journals, Economic Papers and Notes, 13(4), 13-20.

Kilyachkov, A., Chaldaeva, L., & Kilyachkov, N. (2015). Opisaniye izmeneniy mirovogo VVP na korotkikh vremennykh intervalakh s pomoshch'yu diskretnoy dinamicheskoy modeli [Description of World GDP changes at short time intervals by using a discrete dynamic model]. Finansovaya Analitika: Problemy i Resheniya [Financial Analytics: Problems and Solutions], 44(278), 17-31. [in Russian].

Kilyachkov, A., Chaldaeva, L., & Kilyachkov, N. (2016). Diskretnaya dinamicheskaya model' izmeneniya mirovogo VVP [Discrete dynamic model of world GDP changes]. Paper presented in International Scientific and Practical Conference "Modeling in Engineering and Economics", Vitebsk. [in Russian].

Kilyachkov, A., Chaldaeva, L., & Kilyachkov, N. (2017a). Ispol'zovaniye diskretnoy dinamicheskoy modeli dlya opisaniya izmeneniya mirovogo VVP [Using a discrete dynamic model to describe the change in world GDP]. Paper presented in 14th International Conference. "Mathematics. Computer. Education", Pushchino. [in Russian].

Kilyachkov, A., Chaldaeva, L., & Kilyachkov, N. (2017b). Description of world GDP rate changes by using discrete dynamic model. Business and Economic Horizons, 13(1), 77-96. 

Kilyachkov, A., Chaldaeva, L., & Kilyachkov, N. (2018). Application of discrete dynamic model for the assessment of stability of the world economy development. Business and Economic Horizons, 14(1), 75-84. 

Kitchin, J. (1923). Cycles and trends in economic factors. Review of Economic Statistics, 5(1), 10-16. 

Kondratieff, N. (1922). Mirovoye khozyaystvo i yego kon"yunktura vo vremya i posle voyny [The world economy and its conjuncture during and after the war]. Vologda: Regional Department of the State Publishing House. [in Russian].

Kondratieff, N. (1925). Bol'shiye tsikly kon"yunktury [Large conjuncture cycles]. Voprosy Kon"yunktury [Conjuncture Issues], 1(1), 28-79. [in Russian].

Kondratieff, N. (1926). Die langen wellen der konjunktur. Archiv fuer Sozialwissenschaft und Sozialpolitik, 56(3), 573-609.

Kondratieff, N. (1928). Bol'shiye tsikly kon"yunktury [Large conjuncture cycles]. Moscow: Institute of Economics RANION. [in Russian].

Kondratieff, N. (1935). The long waves in economic life. The Review of Economic Statistics, 17(6), 105-115. 

Koopmans, T. (1960). Stationary ordinal utility and impatience. Econometrica, 28(2), 287-309. 

Koopmans, T., & Montias, J. (1971). On the description and comparison of economic systems. In A. Eckstein, ed., Comparison of economic systems (pp. 27-78). Berkeley: Univ. of California Press.

Korotayev, A., & Tsirel, S. (2010). A spectral analysis of world GDP dynamics: Kondratieff waves, Kuznets swings, Juglar and Kitchin cycles in global economic development, and the 2008-2009 economic crisis. Structure and Dynamics, 4(1), 1-55. 

Kuznets, S. (1930). Secular movements in production and prices. Their nature and their bearing upon cyclical fluctuations. Boston: Houghton Mifflin.

Lucas, R. E. Jr., & Prescott, E. C. (1971). Investment under uncertainty. Econometrica, 39, 659-681. 

Malinetsky G. (2009). Matematicheskiye osnovy sinergetiki [Mathematical Foundations of Synergetics]. Moscow: Book House "LIBROKOM". [in Russian].

McFadden, D. (1986). The choice theory approach to market research. Marketing Science, 5(4), 275-297. 

Nash, J. F. (1951). None-cooperative games. Annals of Mathematics, 54(2), 289-295. 

Sekovanov, V. (2013). Elementy teorii fraktal'nykh mnozhestv (5 izd.) [Elements of the theory of fractal sets (5th ed.)]. Moscow: Book House "LIBROKOM". [in Russian].

Simon, H. A. (1959). Theories of decision making in economics and behavioral science. American Economic Review, 49(3), 253-283.

Tinbergen, J. (1956). On the theory of income distribution. Weltwirtschaftliches Archiv, 77, 155-175.

Tobin, J. (1955). A dynamic aggregate model. Journal of Political Economy, 63(2), 103-115. 

Trubetskov D. (2010). Vvedeniye v sinergetiku: Khaos i struktury [Introduction to synergetics: Chaos and structures]. Moscow: Editorial URSS. [in Russian].

World Bank Open Data, GDP growth (annual %), World Data. Retrieved March 18, 2018, from

Keywords Discrete dynamic model, annual rate of world GDP change, attractors, Julia set, basin of attraction
Pages 137-157
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