Skip to main content
Log in

The route to chaos during a pulsation event

  • Published:
Solar Physics Aims and scope Submit manuscript

Abstract

A time series analysis of a pulsation event in solar radio emission provides an evolution from a regular doubly periodic phase to an irregular behaviour. Applying some techniques developed in the theory of nonlinear dynamic systems to this irregular stage suggests that there exists a low-dimensional attractor. Estimates of the maximum Lyapunov exponent give some evidence to deterministic chaos. The sudden transition from a regular to a chaotic structure is identified as a part of the Ruelle-Takens-Newhouse route to chaos which is typical in nonlinear systems. It is checked whether this pulsation event may be interpreted in terms of known pulsation models. Consequences for models, which are suitable to describe such an evolution, are discussed.

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.

Similar content being viewed by others

References

  • Arneodo, A., Coullet, P., and Tresser, C.: 1980, Phys. Letters 79, 259.

    Google Scholar 

  • Aschwanden, M. J.: 1987, Solar Phys. 111, 113.

    Google Scholar 

  • Aschwanden, M. J. and Benz, A. O.: 1988, Astrophys. J., in press.

  • Behringer, R. P.: 1985, Rev. Mod. Phys. 57, 657.

    Google Scholar 

  • Benz, A. O. and Kuijpers, J.: 1976, Solar Phys. 46, 275.

    Google Scholar 

  • Chernov, G.: 1987, private communication.

  • Eckmann, J. P. and Ruelle D.: 1985, Rev. Mod. Phys. 57, 617.

    Google Scholar 

  • Grassberger, P. and Procaccia, I.: 1983, Phys. Rev. Letters 50, 346.

    Google Scholar 

  • Holzfuss, J. and Mayer-Kress, G.: 1986, Dimensions and Entropies in Chaotic Systems, Springer-Verlag, Berlin.

    Google Scholar 

  • Kurths, J.: 1987, Proceedings of the International Conference on Nonlinear Oscillations, Mathematical Society, Budapest.

    Google Scholar 

  • Kurths, J. and Herzel, H.: 1986, Solar Phys. 107, 39.

    Google Scholar 

  • Kurths, J. and Herzel, H.: 1987, Physica 25D, 165.

    Google Scholar 

  • Kurths, J., Auraß, H., and Urpo, S.: 1988, Astron. Astrophys. 191, 359.

    Google Scholar 

  • Mayer-Kress, G. (ed.): 1986, Dimensions and Entropies in Chaotic Systems, Springer-Verlag, Berlin.

    Google Scholar 

  • McLean, D. J.: 1988, private communication.

  • McLean, D. J. and Sheridan, K. V.: 1973, Solar Phys. 32, 485.

    Google Scholar 

  • Meerson, B. I., Sasorov, P. V., and Stepanov, A. V.: 1978, Solar Phys. 58, 165.

    Google Scholar 

  • Newhouse, S., Ruelle, D., and Takens, F.: 1978, Comm. Math. Phys. 64, 35.

    Google Scholar 

  • Roberts, B., Edwin, P. M, and Benz, A. O.: 1984, Astrophys. J. 279, 857.

    Google Scholar 

  • Schuster, H. G.: 1984, Determinsitic Chaos, Chemie Verlag, Weinheim.

    Google Scholar 

  • SGD: 1982, Solar Geophysical Data 451, Part II, Boulder.

  • Sigeti, D. and Horsthemke, W.: 1987, Phys. Rev. A35, 2276.

    Google Scholar 

  • Takens, F.: 1981, ‘Dynamical Systems and Turbulence’, Lecture Notes in Mathematics, Vol. 898, Springer-Verlag, Berlin.

    Google Scholar 

  • Theiler, J.: 1986, Phys. Rev. A34, 2427.

    Google Scholar 

  • Trottet, G., Kerdraon, A., Benz, A. O., and Treumann, R.: 1981, Astron. Astrophys. 93, 29.

    Google Scholar 

  • Urbarz, H.: 1987, private communication.

  • Wolf, A., Swift, J. B., Swinney, H. L., and Vastano, J. A.: 1985, Physica 16D, 285.

    Google Scholar 

  • Zaitsev, V. V. and Stepanov, A. V.: 1975, Astron. Astrophys. 45, 135.

    Google Scholar 

  • Zaitsev, V. V., Stepanov, A. V., and Sterlin, A. M.: 1985, Pisma v Astrofiz. Zh. 11, 463.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Kurths, J., Karlický, M. The route to chaos during a pulsation event. Sol Phys 119, 399–411 (1989). https://doi.org/10.1007/BF00146186

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00146186

Keywords

Navigation