Crisis-induced intermittency due to attractor-widening in a buoyancy-driven solar dynamo

International Journal of Bifurcation and Chaos in Applied Sciences and Engineering

Volumn 13, Issue 8, 2003, Pages 2327-2333

  Ossendrijver, Mathieu ^a   Covas, Eurico ^b  

^a QUEEN MARY UNIVERSITY OF LONDON   (United Kingdom)

^b KIEPENHEUER INSTITUT FÜR SONNENPHYSIK   (Germany)

Author keywords

Chaotic time series; Noise estimation

Indexed keywords

BIFURCATION (MATHEMATICS); BUOYANCY; MAGNETIC FLUX; SWITCHING; TIME SERIES ANALYSIS;

NOISE ESTIMATION;

CHAOS THEORY;

EID: 0242414762     PISSN: 02181274     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218127403007989     Document Type: Article

References (53)

1. Ashwin, P., Buescu, J. & Stewart, I. [1996] "From attractor to chaotic saddle: A tale of transverse instability," Nonlinearity 9, 703-737.
2. Ashwin, P., Covas, E. & Tavakol, R. [1999] "Transverse instability for non-normal parameters," Nonlinearity 9, 563-577.
3. Beer, J., Tobias, S. M. & Weiss, N. O. [1998] "An active sun throughout the Maunder minimum," Solar Phys. 181, 237-249.
4. Blackman, E. & Field, J. [1999] "Resolution of an ambiguity in dynamo theory and its consequences for back-reaction studies," Astrophys. J. 521, 597-601.
5. Blackman, E. & Field, J. [2000] "Constraints on the magnitude in dynamo theory," Astrophys. J. 534, 984-988.
6. Brooke, J. M. [1997] "Breaking of equatorial symmetry in a rotating system," Europhys. Lett. 37, 171-176.
7. Brooke, J. M., Pelt, J., Tavakol, R. & Tworkowski, A. [1998] "Grand minima and equatorial symmetry breaking in axisymmetric dynamo models," A&A 332, 339-352.
8. Charbonneau, P. [2001] "Multiperiodicity, chaos, and intermittency in a reduced model of the solar cycle," Solar Phys. 199, 385-404.
9. Covas, E., Ashwin, P. & Tavakol, R. [1997] "Non-normal parameter blowout bifurcation: An example in a truncated mean-field dynamo model," Phys. Rev. E56, 6451-6458.
10. Covas, E. & Tavakol, R. [1997] "Crisis-induced intermittency in truncated mean field dynamos," Phys. Rev. E55, 6641-6645.
11. Covas, E., Tavakol, R., Tworkowski, A. & Brandenburg, A. [1998] "Axisymmetric mean field dynamos with dynamic and algebraic alpha-quenchings," A&A 329, 350-360.
12. Covas, E. & Tavakol, R. [1999] "Multiple forms of intermittency in partial differential equation dynamo models," Phys. Rev. E80, 5435-5438.
13. Covas, E., Tavakol, R., Ashwin, P., Tworkowski, A. & Brooke, J. M. [2001] "In-out intermittency in partial differential equation and ordinary differential equation models," Chaos 11, 404-409.
14. Cowling, T. G. [1981] "The present status of dynamo theory," Ann. Rev. A&A 19, 115-135.
15. Ditto, W. L. et al. [1989] "Experimental observation of crisis-induced intermittency and its critical exponent," Phys. Rev. Lett. 63, 923-926.
16. Feng, D. L., Zheng, J., Huang, W., Yu, C. X. & Ding, W. X. [1996] "Type-I-like intermittent chaos in multicomponent plasmas with negative ions," Phys. Rev. E54, 2839-2843.
17. Feudel, F., Jansen, W. & Kurths, J. [1993] "Tori and chaos in a nonlinear dynamo model for solar activity," Int. J. Bifurcation and Chaos 3, 131-138.
18. Field, J. et al. [1999] "Nonlinear alpha-effect in dynamo theory," Astrophys. J. 513, 638-651.
19. Finardi, M., Felpp, L., Parisi, J., Holzner, R., Badii, R. & Brun E. [1992] "Topological and metric analysis of heteroclinic crisis in laser chaos," Phys. Rev. Lett. 68, 2989-2991.
20. Gleissberg, W. [1967] "Secularly smoothed data on the minima and maxima of sunspot frequency," Solar Phys. 52, 231-231.
21. Grebogi, C., Ott, E., Romeiras, F. & Yorke, J. A. [1987] "Critical exponents for crisis-induced intermittency," Phys. Rev. A36, 5365-5380.
22. Grebogi, C., Ott, E. & Yorke, J. A. [1982] "Chaotic attractors in crisis," Phys. Rev. Lett. 48, 1507-1510.
23. Knobloch, E. & Landsberg, A. S. [1996] "A new model of the solar cycle," MNRAS 278, 294-302.
24. Knobloch, E., Tobias, S. M. & Weiss, N. O. [1998] "Modulation and symmetry changes in stellar dynamos," MNRAS 297, 1123-1138.
25. Krause, F. & Rädler, K.-H. [1980] Mean-Field Magnetohydrodynamics & Dynamo Theory (Pergamon, Oxford).
26. Küker, M., Arlt, R. & Rd̈iger, G. [1999] "The Maunder minimum as due to magnetic lambda-quenching," A&A 343, 977-982.
27. Metcalfe, G. & Behringer, R. P. [1992] "Observation of chaotic bursting and attractor switching in a fluid," Phys. Rev. A46, 711-714.
28. Ossendrijver, M. A. J. H., Hoyng, P. & Schmitt, D. [1996] "Stochastic excitation and memory of the solar dynamo," A&A 313, 938-948.
29. Ossendrijver, M. A. J. H. [2000] "Grand minima in a buoyancy-driven solar dynamo," A&A 359, 364-372.
30. Parker, E. N. [1979] Cosmic Magnetic Fields (Clarendon Press, Oxford).
31. Platt, N., Spiegel, E. & Tresser, C. [1993] "On-off intermittency: A mechanism for bursting," Phys. Rev. Lett. 70, 279-282.
32. Pomeau, Y. & Manneville, P. [1980] "Intermittent transition to turbulence in dissipative dynamical systems," Commun. Math. Phys. 74, 189-197.
33. Priest, E. [1982] Solar Magnetohydrodynamics, ed. Reidel, D. (Dordrecht).
34. Roberts, P. H. [1995] Lectures on Solar & Planetary Dynamos, eds. Proctor, M. R. E. & Gilbert, A. D. (Cambridge University Press).
35. Schmalz, S. & Stix, M. [1991] "An alpha-omega dynamo with order and chaos," A&A 245, 654-661.
36. Schmitt, D., Schüssler, M. & Ferriz-Mas, A. [1996] "Intermittent solar activity by an on-off dynamo," A&A 311, L1-L4.
37. Schou, J., Antia, H. M., Basu, S. et al. [1998] "Helioseismic studies of differential rotation in the solar envelope by the solar oscillations investigation using the Michelson doppler imager," Ap. J. 505, 390-417.
38. So, B. & Mori, H. [1984] "Power spectra of the intermittency chaos generated by the quadratic tangent bifurcation," Prog. Theor. Phys. 72, 1258-1261.
39. So, B. & Mori, H. [1986] "Asymptotic shapes of power spectra of intermittent chaos near its onset point," Physica D21, 126-130.
40. Sokoloff, D. & Nesme-Ribes, E. [1994] "The Maunder minimum: A mixed-parity dynamo mode?" A&A 288, 293-298.
41. Spiegel, E., Platt, N. & Tresser C. [1993] "The intermittent solar cycle," Geophys. Astrophys. Fluid Dyn. 73, 146-161.
42. Sweet, D., Ott, E., Finn, J. M., Antonsen Jr., T. M. & Lathrop, D. P. [2001] "Blowout bifurcations and the onset of magnetic activity in turbulent dynamos," Phys. Rev. E63, 066211.
43. Tavakol, R. [1978] "Is the sun almost intransitive?" Nature 276, 802-803.
44. Tavakol, R. & Covas, E. [1999] "Intermittency as a possible underlying mechanism for solar and stellar variability," Astron. Soc. Pacific Conf. Series 178, 173-181.
45. Tobias, S. M., Weiss, N. O. & Kirk, V. [1995] "Chaotically modulated stellar dynamos," MNRAS 273, 1150-1166.
46. Tobias, S. M. [1998a] "Symmetry changes of magnetic fields in the sun and other stars," Astron. Soc. Pacific Conf. Series 154, 1349-1359.
47. Tobias, S. M. [1998b] "Relating stellar cycle periods to dynamo calculations," Mon. Not. Roy. Astron. Soc. 296, 653-661.
48. Tobias, S. M., Knobloch, E. & Weiss, N. O. [1999] "Symmetry considerations in stellar dynamos," Astron. Soc. Pacific Conf. Series 178, 185-195.
49. Tworkowski, A., Tavakol, R., Brandenburg, A., Brooke, J. M., Moss, D. & Tuominen, I. [1998] "Intermittent behavior in axisymmetric mean-field dynamo models in spherical shells," MNRAS 296, 287-295.
50. Venkataramani, S. C., Antonsen Jr., T. M., Ott, E. & Sommerer, J. C. [1996] "On-off intermittency: Power spectrum and fractal properties of time series," Physica D96, 66-99.
51. Weiss, N. O., Cattaneo, F. & Jones, C. A. [1984] "Periodic and aperiodic dynamo waves," Geophys. Astrophys. Fluid Dyn. 30, 305-341.
52. Weiss, N. O. [1990] "Periodicity and aperiodicty in solar magnetic activity," Phil. Trans. Roy. Soc. London A330, 617-626.
53. Zeldovich, B. Ya., Ruzmaikin, A. A. & Sokoloff, D. D. [1983] Magnetic Fields in Astrophysics (Gordon & Breach, NY).