Skip to main content
SpringerLink
Log in

Dynamics and adaptive control of a Duopoly advertising model based on heterogeneous expectations

  • Original Paper
  • Published:
Nonlinear Dynamics Aims and scope Submit manuscript

Abstract

This paper discusses a duopoly advertising model based on heterogeneous expectations. Firstly, it points out the unstable region of Nash equilibrium and its influencing factors by analyzing the stability of the improved model. Secondly, it applies the adaptive control method to the chaos of the duopoly advertising model. The control aims are to bring this system into the instability equilibrium point by using minor disturbance of the control parameter. The result of theoretical study and numerical simulation illuminates that the method could successfully lead the chaos track to low cycle track. Moreover, scope of the convergent condition and control intensity are given.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Agiza, H.N., Elsadany, A.A.: Nonlinear dynamics in the Cournot duopoly game with heterogeneous players. Physica A 320, 512–524 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  2. Agiza, H.N., Elsadany, A.A.: Chaotic dynamics in nonlinear duopoly game with heterogeneous players. Appl. Math. Comput. 149, 843–860 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  3. Agiza, H.N., Hegazi, A.S., Elsadany, A.A.: The dynamics of Bowley’s model with bounded rationality. Chaos Solitons Fractals 12, 1705–1717 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  4. Bischi, G.I., Kopel, M.: Equilibrium selection in a nonlinear duopoly game with adaptive expectations. J. Econ. Behav. Organ. 46, 73–100 (2001)

    Article  Google Scholar 

  5. Ott, E., Grebogi, C., Yorke, J.A.: Controlling chaos. Phys. Rev. Lett. 64(11), 1196–1199 (1990)

    Article  MathSciNet  MATH  Google Scholar 

  6. Pyragas, K., Pyragas, V., Kiss, I.I., Hudson, J.L.: Adaptive control of unknown unstable steady states of dynamics systems. Phys. Rev. E 70, 026215 (2004)

    Google Scholar 

  7. Pyragas, K.: Continuous control of chaos by self-controlling feedback. Phys. Lett. A 170, 421–428 (1992)

    Article  Google Scholar 

  8. Agiza, H.N., Hegazi, A.Z., Elsadany, A.A.: Complex dynamics and synchronization of a duopoly game with bounded rationality. Math. Comput. Simul. 58, 133–146 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  9. Bischi, G.I., Gardini, L.S.: Synchronization, intermittency and critical curves in a duopoly game. Math. Comput. Simul. 44, 559–585 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  10. Yao, H.X., Wu, C.Y., Jiang, D.P.: Chaos control in an investment model with straight-line stabilization method. Nonlinear Anal., Real World Appl. 9, 651–662 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  11. Du, J.G., Huang, T.W., Sheng, Z.H.: Analysis of decision-making in economic chaos control. Nonlinear Anal., Real World Appl. 4, 2493–2501 (2009)

    Article  MathSciNet  Google Scholar 

  12. Zhu, J.D., Tian, Y.P.: Nonlinear recursive delayed feedback control for chaotic discrete-time systems. Phys. Lett. A 4(21), 295–300 (2003)

    Article  MathSciNet  Google Scholar 

  13. Kopel, M.: Simple and complex adjustment dynamics in Cournot duopoly model. Chaos Solitons Fractals 12, 2031–2048 (1996)

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Faculty of Science, Jiangsu University, Zhenjiang, Jiangsu, 212013, China

    Juan Ding & Hongxing Yao

  2. Business Administration Academy, Jiangsu University, Zhenjiang, Jiangsu, 212013, China

    Qiang Mei

Authors
  1. Juan Ding
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Qiang Mei
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Hongxing Yao
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Juan Ding.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ding, J., Mei, Q. & Yao, H. Dynamics and adaptive control of a Duopoly advertising model based on heterogeneous expectations. Nonlinear Dyn 67, 129–138 (2012). https://doi.org/10.1007/s11071-011-9964-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11071-011-9964-y

Keywords

Search

Navigation