Skip to main content
Log in

A new detecting method for conditions of existence of Hopf bifurcation

  • Published:
Acta Mathematicae Applicatae Sinica Aims and scope Submit manuscript

Abstract

A new detecting method for the conditions of existence of the Hopf bifurcation is given in terms of the coefficients of the characteristic polynomial at the equilibrium by using the Hopf bifurcation theory and matrix theory. The method is available and important for the study of the existence of the Hopf bifurcation for higher differential equations which often occur in biological models, chemical models, epidemiological models, and models of AIDS.

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

Access this article

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. Feng Beiye. Periodic Travelling-wave Solution of Bruselator.Acta Math. Appl. Sinica, 1988, 4(4): 324–332.

    Article  Google Scholar 

  2. Gantmacher, F.R. The Theory of Matrices, Vol. II. Chelsea, New York, 1959.

    Google Scholar 

  3. In-Ding Hsu and Kazavinoff, N.D. Existence and Stability of Periodic Solutions of a Third-order Nonlinear Autonomous Systems Simulating Immune Response in Animals.Proc. Soc. Edin. (Series A), 1977, 77: 163–175.

    Google Scholar 

  4. Jing Zhujun, Liu Zhengrong and Shen Jiaqi. Hopf Bifurcation and Other Dynamical Behaviors for a Fourth-order Differential Equation in Models of Infections Disease.Acta Math. Appl. Sinica, 1994, 10(4): 401–410.

    Article  Google Scholar 

  5. Jing Zhujun and Liu Zhengrong. Qualitative Analysis for a Mathematical Model of AIDS.Acta Math. Appl. Sinica, 1993, 9(4): 302–316.

    Article  Google Scholar 

  6. Liu Zhengrong and Jing Zhujun. Qualitative Analysis for a Third-order Differential Equation in Model of Chemical System.System Science and Mathematical Sciences, 1992, 5(4): 299–311.

    Google Scholar 

  7. Marsden, J.E. and McCracken, M. The Hopf Bifurcation and Its Applications. Springer-Verlag, New York, 1976.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

This research is supported by the National Science Foundation “Tian Yuan” Terms and LNM, Institute of Mathematics, the Chinese Academy of Sciences.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Shen, J., Jing, Z. A new detecting method for conditions of existence of Hopf bifurcation. Acta Mathematicae Applicatae Sinica 11, 79–93 (1995). https://doi.org/10.1007/BF02012625

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02012625

Key words

Navigation