Skip to main content
SpringerLink
Log in

A method to calculate period doubling bifurcation

  • Published:
Applied Mathematics and Mechanics Aims and scope Submit manuscript

Abstract

Based on physical meaning of Melnikov function, we establish a method to calculate period doubling bifurcation and discuss this kind of bifurcation of soft spring Duffing system and find that the result is analogous to subharmonic bifurcation, that is, period doubling bifurcation will appear if damping is small and amplitude of excitation is big. Thi coincides with facts of physics.

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. Guckenheimer J. and P. Holmes,Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields, Spring-Verlag (1983).

  2. Liu Zheng-rong, Yao Wei-guo and Zhu Zhao-xuan, Road to chaos for a soft spring system under weak periodic excitation,Appl. Math. and Mech. 7, 2 (1986).

    Google Scholar 

  3. Liu Zheng-rong Some bifurcated and chaotic behavior in soft spring Duffing equation,Proceedings of ICNM (1985).

  4. Huberman B.A. and J.P. Crutchfield, Chaotic states of anharmonic system in periodic field,Phys. Rev. Lett.,43, 23 (1979).

    Google Scholar 

  5. Chui S.T. and K.B. Ma, Nature of some chaotic states for Duffing's equation,Phys. Rev. A,26, 4 (1982).

    Article  MathSciNet  Google Scholar 

  6. Liu Zheng-rong, Physical meaning of Melnikov function,Kexue Tongbao (China)30, 22 (1985).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Anhui University, Hefei

    Liu Zheng-rong, Zhou Shi-gang & Liu Er-ning

Authors
  1. Liu Zheng-rong
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Zhou Shi-gang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Liu Er-ning
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Communicated by Xu Zheng-fan

Rights and permissions

Reprints and permissions

About this article

Cite this article

Zheng-rong, L., Shi-gang, Z. & Er-ning, L. A method to calculate period doubling bifurcation. Appl Math Mech 8, 667–671 (1987). https://doi.org/10.1007/BF02458264

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02458264

Keywords

Search

Navigation