Solar Physics

, Volume 199, Issue 2, pp 385–404 | Cite as

Multiperiodicity, Chaos, and Intermittency in a Reduced Model of the Solar Cycle

  • Paul Charbonneau

Abstract

In a recent paper, Durney (2000) has discussed a physically plausible procedure whereby the dynamo equations describing magnetic field regeneration in Babcock–Leighton models of the solar cycle can be reduced to a one-dimensional iterative map. This procedure is used here to investigate the behavior of various dynamo-inspired maps. Durney's explanation of the so-called odd–even effect in sunspot cycle peak amplitudes, which he ascribed to a period-2 limit cycle, is found to be robust with respect the choice of nonlinearity defining the map, and to the action of strong stochastic forcing. In fact, even maps without limit cycles are found to show a strong odd–even signal in the presence of forcing. Some of the stochastically forced maps are found to exhibit a form of on-off intermittency, with periods of activity separated by quiescent phases of low cycle amplitudes. In one such map, a strong odd–even signal is found to be a good precursor to the transition from bursting to quiescent behavior.

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References

  1. Beer, J., Raisbeck, G. M., and Yiou, F.: 1991, in C. P. Sonett, M. S. Giampapa, and M. S. Matthews (eds.), The Sun in Time,p.343Google Scholar
  2. Beer, J., Tobias, S., and Weiss, N.: 1998, Solar Phys. 181, 237.Google Scholar
  3. Caligari, P., Moreno-Insertis, F., and Schüssler, M.: 1995, Astrophys. J. 441, 886.Google Scholar
  4. Charbonneau, P. and Dikpati, M.: 2000, Astrophys. J. 543, 1027.Google Scholar
  5. Dikpati, M. and Charbonneau, P.: 1999, Astrophys. J. 518, 508.Google Scholar
  6. D'Silva, S. and Choudhuri, A.R.: 1993, Astron. Astrophys. 272, 621.Google Scholar
  7. Durney, B. R.: 1997, Astrophys. J. 486, 1065.Google Scholar
  8. Durney, B. R.: 2000, Solar Phys. 196, 421.Google Scholar
  9. Feigenbaum, M. J.: 1978, J. Stat. Phys. 19, 25.Google Scholar
  10. Heagy, J. F., Platt, N., and Hammel, S. M.: 1994, Phys. Rev. E 49, 1140.Google Scholar
  11. Holton, D., and May, R. M.: 1993, in T. Mullin (ed.), Chaos and One-Dimensional Maps, The Nature of Chaos, Oxford University Press, Oxford, p. 69.Google Scholar
  12. Hoyng, P.: 1993, Astron. Astrophys. 272, 321.Google Scholar
  13. Hoyt, D. V. and Schatten, K. H.: 1998, Solar Phys. 181, 491.Google Scholar
  14. Longcope, D. W. and Fisher, G. H.: 1996, Astrophys. J. 458, 380.Google Scholar
  15. Lorenz, E. N.: 1963, J. Atmospheric Sci. 20, 130.Google Scholar
  16. MacGregor, K. B. and Charbonneau, P.: 1997, Astrophys. J. 486, 484.Google Scholar
  17. Moffatt, H. K.: 1978, Magnetic Field Generation in Electrically Conducting Fluids, Cambridge University Press, Cambridge.Google Scholar
  18. Moreno-Insertis, F., Caligari, P., and Schüssler, M.: 1995, Astrophys. J. 452, 894.Google Scholar
  19. Nandy, D. and Choudhuri, A. R.: 2000, preprint.Google Scholar
  20. Ossendrijver, A. J. H. and Hoyng, P.: 1996, Astron. Astrophys. 313, 959.Google Scholar
  21. Ossendrijver, A. J. H., Hoyng, P., and Schmitt, D.: 1996, Astron. Astrophys. 313, 938.Google Scholar
  22. Platt, N., Spiegel, E. A., and Tresser, C.: 1993, Phys. Rev. Letters 70, 279.Google Scholar
  23. Roald, C. B. and Thomas, J. H.: 1997, Monthly Notices Royal Astron. Soc. 288, 551.Google Scholar
  24. Schmalz, S. and Stix, M.: 1991, Astron. Astrophys. 245, 661.Google Scholar
  25. Schmitt, D., Schüssler, M., and Ferriz-Mas, A.: 1996, Astron. Astrophys. 311,L1.Google Scholar
  26. Tworkowski, A., Tavakol, R., Brandenburg, A., Brooke, J. M., Moss, D., and Tuominen, I.: 1998, Monthly Notices Royal Astron. Soc. 296, 287.Google Scholar
  27. Weiss, N. O., Cattaneo, F., and Jones, C. A.: 1984, Geophys. Astrophys. Fluid Dyn. 30, 305.Google Scholar
  28. Wilson, R. M.: 1988, Solar Phys. 117, 269.Google Scholar
  29. Yoshimura, H.: 1979, Astrophys. J. 227, 1047.Google Scholar

Copyright information

© Kluwer Academic Publishers 2001

Authors and Affiliations

  • Paul Charbonneau
    • 1
  1. 1.High Altitude Observatory, National Center for Atmospheric ResearchBoulderU.S.A

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