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Chaos control in an economic model via minimum entropy strategy

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  • Salarieh, Hassan
  • Alasty, Aria

Abstract

In this paper, minimum entropy algorithm for controlling chaos, is applied to a Cournot duopoly with different constant marginal costs, as a discrete-time dynamical system which shows chaotic behavior. The ME control is implemented through delayed feedback. It is assumed that the equations of the dynamical system are not known, so the feedback gain cannot be obtained analytically from the system equations. In the ME method the feedback gain is obtained adaptively 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 for controlling chaos in economic systems with unknown equations.

Suggested Citation

  • Salarieh, Hassan & Alasty, Aria, 2009. "Chaos control in an economic model via minimum entropy strategy," Chaos, Solitons & Fractals, Elsevier, vol. 40(2), pages 839-847.
    • Handle: RePEc:eee:chsofr:v:40:y:2009:i:2:p:839-847
    DOI: 10.1016/j.chaos.2007.08.045
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    References listed on IDEAS

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    1. Salarieh, Hassan & Alasty, Aria, 2008. "Stabilizing unstable fixed points of chaotic maps via minimum entropy control," Chaos, Solitons & Fractals, Elsevier, vol. 37(3), pages 763-769.
    2. Layeghi, Hamed & Arjmand, Mehdi Tabe & Salarieh, Hassan & Alasty, Aria, 2008. "Stabilizing periodic orbits of chaotic systems using fuzzy adaptive sliding mode control," Chaos, Solitons & Fractals, Elsevier, vol. 37(4), pages 1125-1135.
    3. 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.
    4. Bonakdar, Mohammad & Samadi, Mostafa & Salarieh, Hassan & Alasty, Aria, 2008. "Stabilizing periodic orbits of chaotic systems using fuzzy control of Poincaré map," Chaos, Solitons & Fractals, Elsevier, vol. 36(3), pages 682-693.
    5. Mohammad Shahrokhi, 2011. "Adaptive Control of Chaos," Chapters, in: Esteban Tlelo-Cuautle (ed.), Chaotic Systems, IntechOpen.
    6. 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.
    7. Michael Kopel, 1997. "Improving the performance of an economic system: Controlling chaos," Journal of Evolutionary Economics, Springer, vol. 7(3), pages 269-289.
    8. El Naschie, M.S., 2006. "Superstrings, entropy and the elementary particles content of the standard model," Chaos, Solitons & Fractals, Elsevier, vol. 29(1), pages 48-54.
    9. Salarieh, Hassan & Shahrokhi, Mohammad, 2007. "Indirect adaptive control of discrete chaotic systems," Chaos, Solitons & Fractals, Elsevier, vol. 34(4), pages 1188-1201.
    10. 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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    2. Alexeeva, Tatyana A. & Kuznetsov, Nikolay V. & Mokaev, Timur N., 2021. "Study of irregular dynamics in an economic model: attractor localization and Lyapunov exponents," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    3. Akhmet, Marat & Akhmetova, Zhanar & Fen, Mehmet Onur, 2014. "Chaos in economic models with exogenous shocks," Journal of Economic Behavior & Organization, Elsevier, vol. 106(C), pages 95-108.
    4. Yang, Xuenan & Peng, Yu & Xiao, Yue & Wu, Xue, 2019. "Nonlinear dynamics of a duopoly Stackelberg game with marginal costs," Chaos, Solitons & Fractals, Elsevier, vol. 123(C), pages 185-191.
    5. Argentiero, Amedeo & Bovi, Maurizio & Cerqueti, Roy, 2016. "Bayesian estimation and entropy for economic dynamic stochastic models: An exploration of overconsumption," Chaos, Solitons & Fractals, Elsevier, vol. 88(C), pages 143-157.
    6. Kaveh, H. & Salarieh, H. & Hajiloo, R., 2018. "On the control of unknown continuous time chaotic systems by applying Takens embedding theory," Chaos, Solitons & Fractals, Elsevier, vol. 109(C), pages 53-57.

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