How to Cite
Chaparro Guevara, G., & Escot Mangas, L. (2015). Control of chaotic dynamical systems in economics : application in a hyperinflation model. Revista Finanzas Y Política Económica, 7(1), 131–146. https://doi.org/10.14718/revfinanzpolitecon.2015.7.1.7
License

This journal is licensed by a Creative Commons Attribution License (CC BY-NC-SA 4.0) Attribution-Non Commercial 4.0 International. For the CC licenses, the principle isthe creative freedom. This system complements the copyright without opposing it, conscious of its importance in our culture. The content of the articles is the responsibility of each author, and does not compromise in any way, to the journal or the university. It allows the transmission and reproduction of titles, abstracts and full content, with academic, scientific, cultural ends, provided acknowledgment of the respective source. This work cannot be used for commercial purposes. 

Licencia de Creative Commons

They journal does not charge authors for submission or publication.

Abstract

This article examines control of chaotic behavior in a dynamic hyperinflation system using a method proposed by Ott, Grebogi, and Yorke (1990) (OGY method), which seeks to control the chaotic dynamic by slightly perturbing some of the system?s parameters. An example of the method is given through logistic application, and it is subsequently applied in a hyperinflation model (Punita, 2011) to stabilize prices in a stationary one-period orbit.

Keywords:

References

Ahmed, E. y Hassan, S. Z. (2000). Controlling chaos in cournot games. Nonlinear Dynamics Psycology and Life Sciences, 2, 189-194.

Allen, R. G. (1967). Macro-economic theory: a mathematical treatment. Londres: MacMillan.

Bala, V., Majumdar, M. y Mitra, T. (1998). A note on controlling a chaotic tatonnement. Journal of Economic Behavior and Organization, 33, 411-420.

Barbolla, R. y Gómez, J. P. (1987). Control de sistemas macroeconómicos. Estudio de un caso para la economía española. Investigaciones Económicas, 11(1), 101-131.

Bolotin, Y., Tur, A. y Yanovsky, V. (2009). Chaos, concepts, control and constructive use. Berlín: Springer-Berlag.

Cagan, P. (1956). The monetary dynamics of hiperinflation. En M. Friedman (Ed.), Studies in the quantity theory of money (pp. 25-117). Chicago: The University of Chicago Press.

Chen, L. y Chen, G. (2007). Controlling chaos in an economic model. Physica A, 374, 349-358.

Chen, G. y Dong, X. (1993). Control of chaos. A survey. En IEEE Transactions on Circuits and Systems. Preceedings of the 32nd Conference on Decision and Control (pp. 469-474.). San Antonio, Estados Unidos: IEEE.

Fernández Díaz, A., Escot, L. y Grau-Carles, P. (2012). What's new and useful about chaos in economic science. Cuadernos de Trabajo de la Escuela Universitaria de Estadísitca, núm. CT02/2012.

Fernández Díaz, A. y Grau-Carles, P. (2014). Dinámica caótica en economía (teoría y aplicaciones). Madrid: Delta.

Faggini, M. (2009). Chaos and chaotic dynamics in economics. Nonlinear Dynamics, Psychology, and Life Sciences, 13(3), 327-340.

Gandolfo, G. (2009). Economic dynamics. Berlín: Springer-Verlag.

Guégan, D. (2009). Chaos in economics and finance. Annual Reviews in Control, 33(1), 89-93.

Güemes, J. y Matías, M. A. (1993). Control of chaos in unidimensional maps. Physics Letters A, 181, 29-32.

Haag, G., Hagel, T. y Sigg, T. (1997). Active stabilization of a chaotic urban system. Discrete Dynamics in Nature and Society, 1, 127-134.

Holyst, J. A., Hagel, T., Haag, G. y Weidlich, W. (1996). How to control a chaotic economy. Journal of Evolutionary Economics, 6, 31-42.

Holyst, J. A., Hagel, T. y Haag, G. (1997). Destructive role of competition and noise for microeconomics chaos. Chaos, Solitons and Fractals, 7, 1489-1496.

Holyst, J. A.y Urbanowicz, K. (2000). Chaos control in economical model by time delay feedback method. Physica A, 287, 587-598.

Kaas, L. (1998). Stabilizing chaos in a dynamic macroeconomic model. Journal of Economic Behaviour and Organization, 33, 313-332.

Kopel, M. (1997). Improving the performance of an economic system: controlling chaos. Journal of Evolutionary Economics, 7, 269-289.

Lai, Y.-C. (1994). Controlling chaos. Computers in Physics, 8(1), 62-67.

Li, T. y Yorke, J. A. (1975). Period three implies chaos. American Mathematical Monthly, 82, 985-992.

Mendes, V. M. y Mendes, D. A. (2008). Controlling endogenous cycles in an OLG economy by the OGY method. ISCTE Lisbon University Institute Working Paper, 08/08.

Ogata, K (1998). Ingeniería de control moderna. México: Prentice-Hall.

Ott, E., Grebogi, C. y Yorke, J. (1990). Controlling chaos. Physical Review Letters, 64(11), 1196-1199.

Parthasarathy, S. y Sinha, S. (1995). Controlling chaos in unidimensional maps using constant feedback. Physical Review E, 51(6), 6239-6242.

Phillips, A. W. (1954). Stabilization policy in a closed economy. Economic Journal, 64, 290-323.

Punita, R. (2011). Chaos models and the monetary dynamics of hiperinflation. International Business and Economics Research Journal, 10(11), 109-118.

Pyragas, K (1992). Continuous control of chaos by self-controlling feedback. Physics Letters A, 170, 421-428.

Rega, G., Lenci, S. y Thompsom, J. M. (2010). Controlling chaos: the OGY method, its use in mechanics, and an alternative unified framework for control of non-regular dynamics. En M. Thiel et al. (Eds.), Nonlinear dynamics and chaos: advances and perspectives. Berlín: Springer-Verlag.

Romeiras, F., Grebogi, C., Ott, E. y Dayawansa, W. P. (1992). Controlling chaotic dynamical systems. Physics D, 58(165), 81-100.

Salarich, H. y Alasty, A. (2009). Chaos control in an economic model via minimum entropy strategy. Chaos, Solitons and Fractals, 40, 839-847.

Shinbrot, T., Ott, E., Grebogy, C. y Yorke, J. (1990). Using chaos to direct trajectories to targets. Physical Review Letters, 65(26), 3215-3218.

Solé, R. y Manrubia, S. (2001). Orden y caos en sistemas complejos. Barcelona: Universidad Politécnica de Cataluña.

Tena, E. (1990). Control óptimo de sistemas lineales con expectativas racionales. Investigaciones Económicas, 14(1), 85-111.

Timbergen, J. (1952). On the theory of cconomic policy. Ámsterdam: North Holland.

Tustin, A. (1953). The mechanism of economic systems: an approach to the problem of economic stabilization from the point of view of control system engineering. Cambridge: Harvard University Press.

Wieland, C. (2002). Controlling chaos in higher dimensional maps with constant feedback: an analytical approach. Physical Review E, 66, 1-8.

Wieland, C. y Westerhoff, F. H. (2005). Exchange rate dynamics, central bank interventions and chaos control methods. Journal of Economic Behavior & Organization, 4(2), 189-194.

Reference by

Sistema OJS 3 - Metabiblioteca |