Nonlinear Development of Economic System within the Framework of the Lorents Model
DOI:
https://doi.org/10.15407/scin8.03.064Keywords:
determined chaos, model of Lorenz, development of the economic system.Abstract
The known theoretical publications concerning the model of Lorenz, which describes economic processes in framework of the determined chaos theory, had considered. It is experimentally established, that in economic systems a minor alteration of initial parameters can cause change of the outlet results in several tens times that confirms strongly nonlinear character of these systems development. It is shown, that different types of attractors, such as the dot attractors, strange attractor and attractor of a «limiting cycle» type, are formed at different parities of constants of the model under consideration . It expands possibilities of model for practical use in quality of the prognostic tool.
References
Barnett W.A., Hinich M. Has chaos been discovered with economic data? . Nonlinear Dynamics and Evolutionary Economics. 1993. Oxford: Oxford University Press. P. 254-265.
Oxley L. Economics on the Edge of Chaos: How does economics deal with complexity and the implications for systems management. University of Canterbury. New Zealand. 2004.
Ruth M., Hannon B. Modeling dynamic economic systems. Springer-Verlag New York, Inc., 1997.
https://doi.org/10.1007/978-1-4612-2268-2
Sterman J.D. Deterministic Chaos in an Experimental Economic System . Working Paper #2040-88 Alfred P. Sloan School of Management, Massachusetts Institute of Technology, July, 1988. dspace.mit.edu/bitstream/ handle/1721.1/ 47164/...
Dzh. Rosser-ml. Nastojashhee i budushhee jekonofiziki .Voprosy jekonomiki, 30.11.2009. – finanal.ru/?page=1 [in Russian].
Serletis A., Gogas P. Purchasing Power Parity Non linearity and Chaos . Applied Financial Economics. 2000. V. 10. P. 615-622.
https://doi.org/10.1080/096031000437962
Serletis A., Gogas P. Chaos in East European Black Market Exchange Rates . Research in Economics. 1997. V. 51. P. 359-385.
https://doi.org/10.1006/reec.1997.0050
Hiks D. Stoimost' i kapital. Moskva: Progress, 1993. 488 s. [in Russian].
The Economy as a Complex Evolving System . An derson P.W., Arrow K.J. & Pines D. (editors). Redwood City, CA: Addison-Wesley, 1988.
Brock W.A., Hsieh D.A., LeBaron, B. Nonlinear Dynamics, Chaos and Instability: Statistical Theory and Economic Evidence. Cambridge, MA: MIT Press, 1991.
Hommes C.H. Financial markets as nonlinear adaptive evolutionary systems . Quantitative Finance. 2001. V. 1. P. 149-167.
https://doi.org/10.1080/713665542
Lorenz E.N. Deterministic non-periodic flow . Journal of Atmospheric Science. 1963. V. 20. P. 130-141.
https://doi.org/10.1175/1520-0469(1963)020<0130:DNF>2.0.CO;2
Sparrow C. The Lorenz Equation, Bifurcation, Chaos, and Strange Attractors. Berlin-Heidelberg: Springer, 1982.
https://doi.org/10.1007/978-1-4612-5767-7
Andrášik L., Krempaský J. Emergencia deterministického chaosu: ohraničená pasáž v evolúcii ekonomiky . Ekonomický časopis. 2002. No. 6. P. 1076-1099.
Oljems'koj O.I, Jushhenko O.V., Kohan S.V. Synergetychna model' ekonomichnoi' struktury suspil'stva . Zhurnal fizychnyh doslidzhen'. 2004. T. 8, No. 3. S. 268-278 [in Ukrainian].
Zang V.-B. Sinergeticheskaja jekonomika. Vremja i peremeny v nelinejnoj jekonomicheskoj teorii: Per. S angl. Moskva: Mir, 1999. 355 s. [in Russian].
Krempaský J., Kluvánek P. Universality of Lorenz System of Equations . Acta Fac. Paed. Univ. Tyrnaviensis, Ser. C. 2009. No. 13. P. 53-57.
Burlachkov V. Turbulentnost' jekonomicheskih processov: teoreticheskie aspekty . Voprosy jekonomiki. 2009. No. 11. vopreco.ru/rus/archive.files/n11_2009.html [in Russian].
Goodwin R. M. A non-linear theory of the cycle . Rev. Of Economics and Statistics. 1950. V. 32, No. 4. P. 316-332.
https://doi.org/10.2307/1925580
Kozyk V.V., Sydorov Ju.I. Problemy zastosuvannja modeli Lotki-Vol'terra «hyzhak-zhertva» v ekonomichnij praktyci . Nauka ta innovacii'. 2011. No. 1. S. 5-15 [in Ukrainian].
Interv'ju s prof. D. S. Chernavskim, 2003. http:.www.peoples.ru/science/physics/chernavskiy/index.html [in Russian].
Fedotova V. Upravljaemyj haos . «INTELROS – Intelektual'naja Rossija».
http:.www.intelros.ru/2007/02/13/print:page,1,valentina_fedotova_upravlj... [in Russian].
Hodzhson Dzh. Jekonomicheskaja teorija i instituty: Manifest sovremennoj institucional'noj jekonomicheskoj teorii. Moskva: Delo, 2003. 464 s. [in Russian].
