Skip to main content
Log in

Transition to Chaos in Nonlinear Dynamical Systems Through a Subharmonic Cascade of Bifurcations of Two-Dimensional Tori

  • Published:
Differential Equations Aims and scope Submit manuscript

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.

REFERENCES

  1. Berge, P., Pomeau, Y., and Vidal, C., Order Within Chaos. Towards a Deterministic Approach to Turbulence, New York: Wiley, 1986. Translated under the title Poryadok v khaose. O deterministskom podkhode k turbulentosti, Moscow, 2000.

    Google Scholar 

  2. Loskutov, A.Yu. and Mikhailov, A.S., Vvedenie v sinergetiku (Introduction to Synergetics), Moscow, 1990.

  3. Schuster, H.-G., Deterministic Chaos. An Introduction, Weinheim: VCH, 1988. Translated under the title Determinirovannyi khaos: vvedenie, Moscow, 1989.

    Google Scholar 

  4. Chen, G. and Dong, X., From Chaos to Order, World Scientific, 1998.

  5. Sharkovskii, A.N., Ukr. Mat. Zh., 1964, no. 1, pp. 61-71.

    Google Scholar 

  6. Rössler, O.E., Phys. Letters., 1976, vol. 57A, p. 397.

    Google Scholar 

  7. Mackey, M. and Glass, L., Science, 1977, vol. 197, pp. 287-289.

    Google Scholar 

  8. Magnitskii, N.A. and Sidorov, S.V., Differents. Uravn., 2000, vol. 36, no.11, pp. 1488-1492.

    Google Scholar 

  9. Magnitskii, N.A. and Sidorov, S.V., Primenenie instrumentov nelineinoi dinamiki i intellektual'nykh informatsionnykh tekhnologii v ekonomike (Application of Tools of Nonlinear Dynamics and Intelligent Information Technologies to Economics), Moscow, 2002.

  10. Lorenz, E.N., J. Atmos. Sci., 1963, vol. 20, pp. 130-141.

    Google Scholar 

  11. Magnitskii, N.A. and Sidorov, S.V., Differents. Uravn., 2001, vol. 37, no.11, pp. 1494-1506.

    Google Scholar 

  12. Magnitskii, N.A. and Sidorov, S.V., in Nelineinaya dinamika i upravlenie (Nonlinear Dynamics and Control), Emel'yanov, S.V. and Korovin, S.K., Eds., Moscow, 2002, issue 2, pp. 169-184.

  13. Gibbon, J., in Sinergetika (Synergetics), Moscow, 1984, pp. 164-179.

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Magnitskii, N.A., Sidorov, S.V. Transition to Chaos in Nonlinear Dynamical Systems Through a Subharmonic Cascade of Bifurcations of Two-Dimensional Tori. Differential Equations 38, 1703–1708 (2002). https://doi.org/10.1023/A:1023851928014

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1023851928014

Keywords

Navigation