Skip to main content
SpringerLink
Log in

Analyzing the Mechanisms of Loss of Orbital Stability in Mathematical Models of Three-Dimensional Systems

  • Published:
International Applied Mechanics Aims and scope

The field of a variational system and its effect on the loss of orbital stability are analyzed.

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. A. A. Martynyuk and N. V. Nikitina, “On periodic motion and bifurcations in three-dimensional nonlinear systems,” J. Math. Sci., 208, No. 5, 593–606 (2015).

    Article  MathSciNet  MATH  Google Scholar 

  2. N. V. Nikitina, “Lyapunov characteristic exponents,” Dop. NAN Ukrainy, No. 8, 64–71 (2015).

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

    MATH  Google Scholar 

  4. V. S. Anishechenko, V. V. Astakhov, T. E. Vadivasova, O. V. Sosnovtseva, C. W. Wu, and L. Chua, “Dynamics of two coupled Chua’s circuits,” Int. J. Bifurc. Chaos, 5, No. 6, 1677–1699 (1995).

    Article  MathSciNet  MATH  Google Scholar 

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

    MATH  Google Scholar 

  6. A. A. Martynyuk and N. V. Nikitina, “Bifurcations and multi-stabilty of vibrations of three-dimensional system,” Int. Appl. Mech., 51, No. 2, 540–541 (2015).

    Article  Google Scholar 

  7. A. A. Martynyuk and N. B. Nikitina, “On periodical motions in three-dimensional systems,” Int. Appl. Mech., 51, No. 4, 369–379 (2015).

    Article  ADS  MATH  Google Scholar 

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

    Book  MATH  Google Scholar 

  9. V. V. Nemytskii and V. V. Stepanov, Qualitative Theory of Differential Equation, Princeton Univ. Press, Princeton (1960).

    MATH  Google Scholar 

  10. N. V. Nikitina and V. N. Sidorets, “Bifmurcation processes in a physical model,” Int. Appl. Mech., 52, No. 3, 326–332 (2016).

    Article  ADS  MATH  Google Scholar 

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

    Book  MATH  Google Scholar 

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

    Book  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

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

    N. V. Nikitina

Authors
  1. N. V. Nikitina
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to N. V. Nikitina.

Additional information

Translated from Prikladnaya Mekhanika, Vol. 53, No. 6, pp. 121–132, November–December, 2017.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Nikitina, N.V. Analyzing the Mechanisms of Loss of Orbital Stability in Mathematical Models of Three-Dimensional Systems. Int Appl Mech 53, 716–726 (2017). https://doi.org/10.1007/s10778-018-0853-7

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10778-018-0853-7

Keywords

Search

Navigation