Skip to main content
SpringerLink
Log in

Bifurcations and Multistability of the Oscillations of a Three-Dimensional System

  • Published:
International Applied Mechanics Aims and scope

A generator with inertial nonlinearity is considered. The bifurcations are illustrated by simple examples using the comparison method and Lyapunov functions

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. V. S. Anishchenko, Complex Oscillations in Simple Systems [in Russian], Nauka, Moscow (1990).

  2. S. A. Koblyanskiy, A. V. Shabunin, and V. V. Astakhov, “Forced synchronization of periodic oscillations in a system with phase multistability,” Rus. J. Nonlin. Dyn., 6, No. 2, 277–289 (2010).

    Google Scholar 

  3. A. A. Martynyuk and A. Yu. Obolenskii, “Stability of solutions of Wazewski’s autonomous systems,” Diff. Uravn., 16, No. 8, 1392–1407 (1980).

    MathSciNet  Google Scholar 

  4. N. V. Nikitina, Nonlinear Systems with Complex and Chaotic Behavior of Trajectories [in Russian], Feniks, Kyiv (2012).

  5. V. S. Anishchenko, S. V. Astakhov, and T. E. Vadivasova, “Diagnostics of the degree of noise influence on a nonlinear system using relative metric entropy,” Regul. Chaot. Dynam., 15, No. 2–3, 263–276 (2010).

    MathSciNet  ADS  Google Scholar 

  6. V. A. Krys’ko, T. V. Yakovleva, V. V. Dobriyan, and I. V. Papkova, “Wavelet-analysis-based chaotic synchronization of vibrations of multilayer mechanical structures,” Int. Appl. Mech., 50, No. 6, 706–720 (2014).

    Article  MathSciNet  ADS  Google Scholar 

  7. G. A. Leonov, Strange Attractors and Classical Stability Theory, University Press, St. Peterburg (2008).

    Google Scholar 

  8. A. A. Martynyuk, “Asymptotic stability criterion for nonlinear monotonic systems and its applications (review),” Int. Appl. Mech., 47, No. 5, 475–534 (2011).

    Article  MATH  MathSciNet  ADS  Google Scholar 

  9. A. A. Martynyuk and N. V. Nikitina, “Bifurcation processes in periodically perturbed systems,” Int. Appl. Mech., 49, No. 1, 114–121 (2013).

    Article  ADS  Google Scholar 

  10. A. A. Martynyuk and N. V. Nikitina, “Stability and bifurcation in a model of the magnetic field of the Earth,” Int. Appl. Mech., 50, No. 6, 721–729 (2014).

    Article  MathSciNet  ADS  Google Scholar 

  11. Yu. I. Neimark and P. S. Landa, Stochastic and Chaotic Oscillations, Kluwer, Dordrecht (1992).

  12. L. P. Shilnikov, A. L. Shilnikov, D. V. Turaev, and L. O. Chua, Methods of Qualitative Theory in Nonlinear Dynamics, Part I, World Scientific (1998).

  13. L. P. Shilnikov, A. L. Shilnikov, D. V. Turaev, and L. O. Chua, Methods of Qualitative Theory in Nonlinear Dynamics, Part II, World Scientific (2001).

Download references

Author information

Authors and Affiliations

  1. S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, 3 Nesterova St, Kyiv, 03057, Ukraine

    A. A. Martynyuk & N. V. Nikitina

Authors
  1. A. A. Martynyuk
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. N. V. Nikitina
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to A. A. Martynyuk.

Additional information

Translated from Prikladnaya Mekhanika, Vol. 51, No. 2, pp. 122–132, March–April 2015.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Martynyuk, A.A., Nikitina, N.V. Bifurcations and Multistability of the Oscillations of a Three-Dimensional System. Int Appl Mech 51, 223–232 (2015). https://doi.org/10.1007/s10778-015-0687-5

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10778-015-0687-5

Keywords

Search

Navigation