Skip to main content
SpringerLink
Log in

Hopf bifurcation and chaos of financial system on condition of specific combination of parameters*

  • Published:
Journal of Systems Science and Complexity Aims and scope Submit manuscript

Abstract

Exponential stability of the first order singular distributed parameter systems is discussed in the light of degenerate semi-group methods, which is described by the abstract developing equation in Hilbert space. The necessary and sufficient conditions concerning the exponential stability of the first order singular distributed parameter systems 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. L. Joder, and M. L. Femandez, An implicit difference method for the numerical solution of coupled system of partial differential equations, Appl. Math. Comput., 1991, 46: 127–134.

    Article  Google Scholar 

  2. F. L. Lewis, A review of 2-D implicit systems, Automatic, 1992, 28(2): 345–354.

    Article  Google Scholar 

  3. Y. Hu, S. G. Peng, and X. J. Li, Maximum principle for optimal control problem of nonlinear generalized systems-infinite dimensional case, Acta Mathmaticae Applicatae Sinica, 1992, 15(1): 99–104.

    Google Scholar 

  4. Z. Trzaska, and W. Marszalek, Singular distributed parameter systems, IEE Control Theory and Applications, 1993, 40(5): 305–308.

    Google Scholar 

  5. Z. Q. Ge, G. T. Zhu, and Y. H. Ma, Pole assignment for the first order coupled generalized control system, Control Theory and Application, 2000, 17(3): 379–383.

    Google Scholar 

  6. Z. Q. Ge, and Y. H. Ma, Pole assignment of the coupled generalized system, Systems Science, 2000, 26(3): 5–14.

    Google Scholar 

  7. Z. Q. Ge, and Y. H. Ma, Pole assignment of the first order generalized distributed parameter system, Chinese Annals of Mathematics, 2001, 22(6): 729–734.

    Google Scholar 

  8. Z. Q. Ge, Stabilization of the first order generalized distributed parameter system, in Proceedings of the [Trial mode]th World Congress on Intelligent Control and Automation, Shanghai, P. R. China, June 10–14, 2002, 2212–2216.

  9. Z. Q. Ge, G. T. Zhu, and Y. H. Ma, Spectrum distribution of the second order generalized system, Applied Mathematics and Mechanics, 2003, 24(10): 1224–1232.

    Article  Google Scholar 

  10. Z. Q. Ge, Pole assignment by feedback control of the second order coupled singular distributed parameter systems, Control and Cybernetics, 2004, 33(4): 551–562

    Google Scholar 

  11. Z. Q. Ge, X. Y. Xu, and G. T. Zhu, Asymptotical stability by feedback control for a class of the first order singular control system, Dynamics of Continuous, Discrete and Impulsive Systems Series B: Applications and Algorithms, 2006, 13(Part 2 Suppl. S): 574–577.

    Google Scholar 

  12. Z. Q.Ge, G. T.ZhuState feedback and pole assignment for a class of the second order coupled generalized distributed parameter systemsDynamics of Continuous, Discrete and Impulsive Systems Series B: Applications and Algorithms, 2006, 13Part 1 Suppl. S1–5

    Google Scholar 

  13. Z. Q.Ge, G. T.Zhu, D. X.FengOn the stabilization by feedback of the second order singular distributed parameter control systemsDynamics of Continuous, Discrete and Impulsive Systems Series B: Applications and Algorithms, 2006, 13Part 1 Suppl. S116–120

    Google Scholar 

  14. F.Liu, Z. Q.Ge, X. Y.Xuthe feedback control and pole assignment of the second order singular distributed parameter control systemsDynamics of Continuous, Discrete and Impulsive Systems Series B: Applications and Algorithms, 2006, 13Part 1 Suppl. S256–260

    Google Scholar 

  15. I. V. Melnikova and A. Filinkov, Abstract Cauchy Problem: Three Approaches, Chapman [Trial mode] Hall, CRC, 2001, 86–89.

Download references

Author information

Authors and Affiliations

  1. Department of Applied Mathematics, Xi’an Jiaotong University, Xi’an, 710049, China

    Zhaoqiang GE

  2. Institute of Systems Science, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100080, China

    Guangtian ZHU & Dexing FENG

Authors
  1. Zhaoqiang GE
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Guangtian ZHU
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Dexing FENG
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Zhaoqiang GE.

Additional information

*This research is supported by the National Natural Science Foundation of China under Grant No. 60674018.

Rights and permissions

Reprints and permissions

About this article

Cite this article

GE, Z., ZHU, G. & FENG, D. Hopf bifurcation and chaos of financial system on condition of specific combination of parameters*. J Syst Sci Complex 21, 260–266 (2008). https://doi.org/10.1007/s11424-008-9109-8

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11424-008-9109-8

Keywords

Search

Navigation