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NONLINEAR OPTIMIZATION OF THE CHAOTIC MARKET DYNAMICS
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NONLINEAR OPTIMIZATION OF THE CHAOTIC MARKET DYNAMICS
Annotation
PII
S042473880000616-6-1
Publication type
Article
Status
Published
Authors
Alexander Loskutov 
Edition
Issue №3
Pages
58-70
Abstract
In the framework of the theory of dynamic systems, the problem of stabilization of the chaoticbehavior of the goods market formed by competing firms is considered. The analysis isbased on the study of a fairly simple economic model of two firms operating inthe same market, which conduct an active and asymmetric investment strategy.In the parameter space of this model, the regions corresponding to its chaoticbehavior are found. It is shown that by small changes in the parameters responsible for investment efficiency, it becomes possible to suppress chaos and deduce the dynamics of bothswitching to a periodic mode of operation. As a result, the market situation stabilizes and both firms on average begin to make large profits. However, toget this result, it is sufficient that onlyone firm implements the described policy. Generalizations of the obtained conclusions are given for the case of a large numberof market participants. Elements of the mathematical theory of stabilization of the chaotic behavior of dynamical systems are presented.
Keywords
chaotic dynamics, market for goods, suppression of chaos, competition model
Date of publication
01.07.2010
Number of purchasers
2
Views
856
Readers community rating
0.0 (0 votes)
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Alekseev V.V., Loskutov A.Yu. (1987): Upravlenie sistemoj so strannym attraktorom posredstvom periodicheskogo parametricheskogo vozdejstviya // Doklady Akademii nauk SSSR. T. 293. № 6.
 Loskutov A.Yu., Dzhanoev A.R. (2004): Podavlenie khaosa v okrestnosti separatrisy // ZhEhTF. T. 125. Vyp. 5.
 Loskutov A.Yu., Mikhajlov A.S. (2007): Osnovy teorii slozhnykh sistem. M.: RKhD.
 Loskutov A.Yu., Shishmarev A.I. (1993): Ob odnom svojstve semejstva kvadratichnykh otobrazhenij pri parametricheskom vozdejstvii // Uspekhi mat. nauk. T. 48. № 1.
 Nejmark Yu.I. (1978): Dinamicheskie sistemy i upravlyaemye protsessy. M.: Nauka.
 Pu T. (2002): Nelinejnaya ehkonomicheskaya dinamika. M.; Izhevsk: URSS.
 Ahmed E., Hassan S.Z. (2000): On Controlling Chaos in Cournot-Games with Two and Three Competitors // Nonlinear Dynamics, Phychology, and Life Sciences. Vol. 4. № 2.
 Assaf IV D., Gadbois S. (1992): Defi nition of Chaos // American Math. Monthly. Vol. 99.
 Banks J., Brooks J., Cairns G., Davis G., Stacey P. (1992): On Devaney’s Defi nition of Chaos // American Math. Monthly. Vol. 99.
 Boccaletti S., Grebogi C., Lai Y.-C., Mancini H., Maza D. (2000): The Control of Chaos: Theory and Applications // Physics Reports. Vol. 329.
 Devaney R.L. (1993): An Introduction to Chaotic Dynamical Systems. N.Y.; Amsterdam: Addison-Wesley Publishing Co.
 Feichtinger G. (1992): Economic Evolution and Demographic Change. Berlin: Springer.
 Holyst J.A., Hagel T., Haag G., Weidlich W. (1996): How to Control a Chaotic Economy? // J. of Evolutionary Econ. Vol. 6.
 Holyst J.A., Urbanowicz K. (2000): Chaos Control in Economical Model by Time-Delayed Feedback Method // Physica A. Vol. 287.
 Holyst J.A., Zebrowska M., Urbanowicz K. (2001): Observations of Deterministic Chaos in Financial TimeSeries by Recurrence Plots, Can One Control Chaotic Economy? // The European Physical J. B – CondensedMatter and Complex Systems. Vol. 20.
 Knudsen C. (1994): Chaos without Periodicity // American Math. Monthly. Vol. 101.
 Kopel M. (1997): Improving the Performance of an Economic System: Controlling Chaos // J. of Evolutionary Econ. Vol. 7.
 Kostelich E., Grebogi C., Ott E., Yorke J.A. (1993): Higher Dimensional Targetting // Physical Rev. E. Vol. 47.
 Loskutov A. (1993): Dynamics Control of Chaotic Systems by Parametric Destochastization // J. Physics A. Vol. 26. № 18.
 Loskutov A. (1995): Non-Feedback Controlling Complex Behaviour of Dynamical Systems: An Analytic Approach. In: “Nonlinear Dynamics: New Theoretical and Applied Results”. Berlin: Academie Verlag.
 Loskutov A. (2001): Chaos and Control in Dynamical Systems // Computational Math. and Modeling. Vol. 12. № 4.
 Loskutov A. (2006): Parametric Perturbations and Non-Feedback Controlling Chaotic Motion // Discrete and Continuous Dynamical Systems. Series B. Vol. 6. № 5.
 Loskutov A., Shishmarev A.I. (1994): Control of Dynamical Systems Behavior by Parametric Perturbations: an Analytic Approach // Chaos. Vol. 4. № 2.
 Loskutov A., Tereshko V.M., Vasiliev K.A. (1996): Stabilization of Chaotic Dynamics of One-Dimensional Maps // The International J. of Bifurcation and Chaos. Vol. 6. № 4.
 Meucci R., Gadomski W., Ciofi ni M., Arecchi F.T. (1994): Experimental Control of Chaos by Weak Parametric Perturbations // Physics Rev. E. Vol. 49. № 4.
 Mikhailov A.S., Loskutov A. (1995): Chaos and Noise. Berlin: Springer. Ott E., Grebogi C., Yorke J.A. (1990): Controlling Chaos // Physics Rev. Lett. Vol. 64.
 Schwalger T., Dzhanoev A., Loskutov A. (2006): May Chaos Always Be Suppressed by Parametric Perturbations? // Chaos. № 16.
 Shinbrot T., Grebogi C., Ott E., Yorke J.A. (1992): Using Chaos to Target Stationary States of Flows // Physics Lett. A. Vol. 169.
 Shinbrot T., Ott E., Grebogi C., Yorke J.A. (1990): Using Chaos to Direct Trajectories to Targets // Physics Rev. Lett. Vol. 65.
 Shinbrot T., Ott E., Grebogi C., Yorke J.A. (1992): Using Chaos to Direct Orbits to Targets in Systems Describable by a One-Dimensional Map // Physics Rev. A. Vol. 45. № 6.
 Zhang W.-B. (1997): Synergetic Economics. Berlin: Springer.

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