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On Existence of Attractors in Some Three-Dimensional Systems

  • N. V. NikitinaEmail author
Article

Two cases of existence of attractors in the basic models of a three-dimensional system are analyzed.

Keywords

two-disk dynamo model Rössler model bifurcation chaos 

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References

  1. 1.
    A. E. Cook and P. H. Roberts, “The Rikitake two-disc dynamo system,” Math. Proc. Cambridge Philos. Soc., 68, No. 2, 547–569 (1970).ADSCrossRefGoogle Scholar
  2. 2.
    N. V. Nikitina, Nonlinear Systems with Complex and Chaotic Behavior of Trajectories [in Russian], Feniks, Kyiv (2012).Google Scholar
  3. 3.
    N. V. Nikitina, “Symmetry principle in three-dimensional systems,” Dop. NAN Ukrainy, No. 7, 21–28 (2017).Google Scholar
  4. 4.
    G. A. Leonov, Strange Attractors and Classical Stability Theory, St. Peterburg Univ. Press, St. Peterburg (2008).zbMATHGoogle Scholar
  5. 5.
    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, 721–731 (2014).ADSCrossRefzbMATHGoogle Scholar
  6. 6.
    A. A. Martynyuk and N. V. Nikitina, “Bifurcations and multi-stability of the oscillations of a three-dimensional system,” Int. Appl. Mech., 51, No. 2, 223–232 (2015).ADSCrossRefzbMATHGoogle Scholar
  7. 7.
    A. A. Martynyuk and N. V. Nikitina, “On periodical motions in three-dimensional systems,” Int. Appl. Mech., 51, No. 4, 369–379 (2015).ADSCrossRefzbMATHGoogle Scholar
  8. 8.
    Yu. I. Neimark and P. S. Landa, Stochastic and Chaotic Oscillations, Kluwer, Dordrecht (1992).CrossRefzbMATHGoogle Scholar
  9. 9.
    V. V. Nemytskii and V. V. Stepanov, Qualitative Theory of Differential Equation, Princeton Univ. Press, Princeton (1960).zbMATHGoogle Scholar
  10. 10.
    O. E. Rössler, “Chemical turbulence: chaos in a simple reaction-diffusion system,” Z. Naturforsch, 31a, No. 10, 1168–1172 (1976).ADSGoogle Scholar
  11. 11.
    L. P. Shilnikov, A. L. Shilnikov, D. V. Turaev, and L. O. Chua, Methods of Qualitative Theory in Nonlinear Dynamics, Part I, World Scientific, Singapore (1998).CrossRefzbMATHGoogle Scholar
  12. 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).CrossRefzbMATHGoogle Scholar

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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.S. P. Timoshenko Institute of MechanicsNational Academy of Sciences of UkraineKyivUkraine

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