Geodesic
Global Schumpeterian dynamics with structural variations
Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, Tome 12 (2019) no. 3, pp. 17-27 Cet article a éte moissonné depuis la source Math-Net.Ru

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In this paper, we present the investigations developing the schumpeterian theory of endogenous evolution of economic systems. The proposed approach allows to simulate the emergence and propagation of new technologies. We develop a mathematical model of dynamics of sector capital distribution over efficiency levels on the base of the system of nonlinear differential equations. In order to take into account the boundedness of the economic growth conditioned by the boundedness of the markets, the resource base and other factors, we introduce the notion of economical niche volume. The scenario of the emergence of the new highest efficiency level is proposed. In order to simulate the process of the emergence of the new highest efficiency level, the notion of intellectual capital is proposed. According to the proposed scenario, the new level emerges when the intellectual capital achieves the threshold value. Herewith, the dimension of the dynamic system is varied. The necessary condition for the functioning of the new level is formulated. The invariant set of the dynamic system is defined. The local stability of the equilibria is investigated. The global stability of the dynamic system is established on the base of a geometrical method. The proposed models allow to evaluate and predict the dynamics of the technological levels of the economic sector firms development.
Keywords: dynamic systems, Schumpeterian dynamics, stability. 
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A. N. Kirillov; A. M. Sazonov. Global Schumpeterian dynamics with structural variations. Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, Tome 12 (2019) no. 3, pp. 17-27. http://geodesic.mathdoc.fr/item/VYURU_2019_12_3_a1/

[1] J. Schumpeter, Theorie der wirtschaftlichen Entwicklung, Verlag von Duncker und Humblot, Leipzig, 1911 (in German)

[2] Acemoglu D., Cao D., “Innovation by Entrants and Incumbents”, HKS Faculty Research Working Paper Series, 2012, no. 238, 1–13

[3] Christensen C., Raynor M., The Innovator's Solution, Harvard Business School Press, Harvard, 2003

[4] Glazev S. Yu., The Theory of the Long-Run Technical and Economic Development, VlaDar, M., 1993 (in Russian)

[5] Klimek P., Hausmann R., Thurner S., “Empirical Confirmation of Creative Destruction from World Trade Data”, HKS Faculty Research Working Paper Series, 2012, no. 238, 1–13

[6] Iwai K., “Schumpeterian Dynamics. Part 1: An Evolutionary Model of Innovation and Imitation”, Journal of Economic Behavior and Organization, 5:2 (1984), 159–190 | DOI

[7] Iwai K., “Schumpeterian Dynamics. Part 2: Technological Progress, Firm Growth and “Economic Selection””, Journal of Economic Behavior and Organization, 5:3–4 (1984), 321–351 | DOI

[8] Gelman L. M., Levin M. I., Polterovich V. M., Spivak V. A., “Modelling of the Dynamics of Firms Distribution in Accordance with Efficiency Levels (Ferrous Metal Industry Case)”, Economics and Mathematical Methods, 29:24 (1993), 460–469 (in Russian) | MR

[9] Polterovich V. M., Khenkin G. M., “An Evolutionary Model with Interaction between Development and Adoption of New Technologies”, Economics and Mathematical Methods, 1988, no. 24, 1071–1083 (in Russian)

[10] Polterovich V. M., “The Theory of Endogenous Economic Growth and Equations of Mathematical Physics”, The Journal of the New Economic Association, 2017, no. 2 (34), 193–201 | DOI

[11] Khenkin G. M., Shananin A. A., “Mathematical Modelling of the Schumpeterian Dynamics of Innovation”, Mathematical Modelling, 26:3 (2014), 3–19

[12] Kirillov A. N., Sazonov A. M., “Global Stability in Model of Non-Linear Schumpeterian Dynamics”, Transactions of KarRC RAS, 2018, no. 7, 34–40 | DOI | MR | Zbl