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Delayed feedback control via minimum entropy strategy in an economic model

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  • Salarieh, Hassan
  • Alasty, Aria

Abstract

In this paper minimum entropy (ME) algorithm for controlling chaos, is applied to the Behrens–Feichtinger model, as a discrete-time dynamic system which models a drug market. The ME control is implemented through delayed feedback. It is assumed that the dynamic equations of the system are not known, so the proper feedback gain cannot be obtained analytically from the system equations. In the ME approach the feedback gain is obtained and adapted in such a way that the entropy of the system converges to zero, hence a fixed point of the system will be stabilized. Application of the proposed method with different economic control strategies is numerically investigated. Simulation results show the effectiveness of the ME method to control chaos in economic systems with unknown dynamic equations.

Suggested Citation

  • Salarieh, Hassan & Alasty, Aria, 2008. "Delayed feedback control via minimum entropy strategy in an economic model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(4), pages 851-860.
    • Handle: RePEc:eee:phsmap:v:387:y:2008:i:4:p:851-860
    DOI: 10.1016/j.physa.2007.09.049
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    References listed on IDEAS

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    1. Alasty, Aria & Salarieh, Hassan, 2007. "Nonlinear feedback control of chaotic pendulum in presence of saturation effect," Chaos, Solitons & Fractals, Elsevier, vol. 31(2), pages 292-304.
    2. Mohammad Shahrokhi, 2011. "Adaptive Control of Chaos," Chapters, in: Esteban Tlelo-Cuautle (ed.), Chaotic Systems, IntechOpen.
    3. Chen, Liang & Chen, Guanrong, 2007. "Controlling chaos in an economic model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 374(1), pages 349-358.
    4. Michael Kopel, 1997. "Improving the performance of an economic system: Controlling chaos," Journal of Evolutionary Economics, Springer, vol. 7(3), pages 269-289.
    5. Hołyst, Janusz A & Urbanowicz, Krzysztof, 2000. "Chaos control in economical model by time-delayed feedback method," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 287(3), pages 587-598.
    6. Salarieh, Hassan & Shahrokhi, Mohammad, 2007. "Indirect adaptive control of discrete chaotic systems," Chaos, Solitons & Fractals, Elsevier, vol. 34(4), pages 1188-1201.
    7. Weidlich, Wolfgang & Braun, Martin, 1992. "The Master Equation Approach to Nonlinear Economics," Journal of Evolutionary Economics, Springer, vol. 2(3), pages 233-265, October.
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    Cited by:

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    2. Hajipour, Ahamad & Hajipour, Mojtaba & Baleanu, Dumitru, 2018. "On the adaptive sliding mode controller for a hyperchaotic fractional-order financial system," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 497(C), pages 139-153.

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