In-out intermittency in partial differential equation and ordinary differential equation models

Chaos

Volumn 11, Issue 2, 2001, Pages 404-409

  Covas, Eurico ^a   Tavakol, Reza ^a   Ashwin, Peter ^b   Tworkowski, Andrew ^c   Brooke, John M ^d  

^a UNIVERSITY COLLEGE LONDON   (United Kingdom)

^b UNIVERSITY OF EXETER   (United Kingdom)

^c UNIVERSITY OF LONDON   (United Kingdom)

^d National Computing Centre   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0035374322     PISSN: 10541500     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.1374243     Document Type: Article

References (68)

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36. There are also arguments showing that the mean-field dynamo equation (2) remains valid in a qualitative way, see for example, T. G. Cowling, Annu. Rev. Astron. Astrophys. 19, 115 (1981); E. Priest, in Solar Magnetohydrodynamics, edited by D. Reidel, Dordrecht (1982) and references therein; in the sense that different derivations arrive at basically the same equation, see for example, E. N. Parker, Cosmic Magnetic Fields (Clarendon, Oxford, 1979); see also J. Field et al. Astrophys. J. 513, 638 (1999); E. Blackman and J. Field, ibid. 521, 597 (1999); 534, 984 (2000) which suggest that some of these criticisms of enhanced suppression might be challenged.
37. There are also arguments showing that the mean-field dynamo equation (2) remains valid in a qualitative way, see for example, T. G. Cowling, Annu. Rev. Astron. Astrophys. 19, 115 (1981); E. Priest, in Solar Magnetohydrodynamics, edited by D. Reidel, Dordrecht (1982) and references therein; in the sense that different derivations arrive at basically the same equation, see for example, E. N. Parker, Cosmic Magnetic Fields (Clarendon, Oxford, 1979); see also J. Field et al. Astrophys. J. 513, 638 (1999); E. Blackman and J. Field, ibid. 521, 597 (1999); 534, 984 (2000) which suggest that some of these criticisms of enhanced suppression might be challenged.
38. There are also arguments showing that the mean-field dynamo equation (2) remains valid in a qualitative way, see for example, T. G. Cowling, Annu. Rev. Astron. Astrophys. 19, 115 (1981); E. Priest, in Solar Magnetohydrodynamics, edited by D. Reidel, Dordrecht (1982) and references therein; in the sense that different derivations arrive at basically the same equation, see for example, E. N. Parker, Cosmic Magnetic Fields (Clarendon, Oxford, 1979); see also J. Field et al. Astrophys. J. 513, 638 (1999); E. Blackman and J. Field, ibid. 521, 597 (1999); 534, 984 (2000) which suggest that some of these criticisms of enhanced suppression might be challenged.
39. There are also arguments showing that the mean-field dynamo equation (2) remains valid in a qualitative way, see for example, T. G. Cowling, Annu. Rev. Astron. Astrophys. 19, 115 (1981); E. Priest, in Solar Magnetohydrodynamics, edited by D. Reidel, Dordrecht (1982) and references therein; in the sense that different derivations arrive at basically the same equation, see for example, E. N. Parker, Cosmic Magnetic Fields (Clarendon, Oxford, 1979); see also J. Field et al. Astrophys. J. 513, 638 (1999); E. Blackman and J. Field, ibid. 521, 597 (1999); 534, 984 (2000) which suggest that some of these criticisms of enhanced suppression might be challenged.
40. There are also arguments showing that the mean-field dynamo equation (2) remains valid in a qualitative way, see for example, T. G. Cowling, Annu. Rev. Astron. Astrophys. 19, 115 (1981); E. Priest, in Solar Magnetohydrodynamics, edited by D. Reidel, Dordrecht (1982) and references therein; in the sense that different derivations arrive at basically the same equation, see for example, E. N. Parker, Cosmic Magnetic Fields (Clarendon, Oxford, 1979); see also J. Field et al. Astrophys. J. 513, 638 (1999); E. Blackman and J. Field, ibid. 521, 597 (1999); 534, 984 (2000) which suggest that some of these criticisms of enhanced suppression might be challenged.
41. There are also arguments showing that the mean-field dynamo equation (2) remains valid in a qualitative way, see for example, T. G. Cowling, Annu. Rev. Astron. Astrophys. 19, 115 (1981); E. Priest, in Solar Magnetohydrodynamics, edited by D. Reidel, Dordrecht (1982) and references therein; in the sense that different derivations arrive at basically the same equation, see for example, E. N. Parker, Cosmic Magnetic Fields (Clarendon, Oxford, 1979); see also J. Field et al. Astrophys. J. 513, 638 (1999); E. Blackman and J. Field, ibid. 521, 597 (1999); 534, 984 (2000) which suggest that some of these criticisms of enhanced suppression might be challenged.
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47. With different algebraic forms of the α effect (see Ref. 16 for details).
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62. S. Schmalz and M. Stix, Astron. Astrophys. 245, 654 (1991); F. Feudel, W. Jansen, and J. Kurths, Int. J. Bifurcation Chaos Appl. Sci. Eng. 3, 131 (1993); M. A. J. H. Ossendrijver, P. Hoyng, and D. Schmitt, Astron. Astrophys. 313, 938 (1996); D. Schmitt, M. Schüssler, and A. Ferriz-Mas, ibid. 311, L1 (1996); J. M. Brooke, J. Pelt, R. Tavakol, and A. Tworkowski, ibid. 332, 339 (1998); E. Covas and R. Tavakol, Phys. Rev. E 60, 5435 (1999); M. Küker, R. Arlt, and G. Rd̈iger, Astron. Astrophys. 343, 977 (1999); M. A. J. H. Ossendrijver, ibid. 359, 364 (2000).
63. S. Schmalz and M. Stix, Astron. Astrophys. 245, 654 (1991); F. Feudel, W. Jansen, and J. Kurths, Int. J. Bifurcation Chaos Appl. Sci. Eng. 3, 131 (1993); M. A. J. H. Ossendrijver, P. Hoyng, and D. Schmitt, Astron. Astrophys. 313, 938 (1996); D. Schmitt, M. Schüssler, and A. Ferriz-Mas, ibid. 311, L1 (1996); J. M. Brooke, J. Pelt, R. Tavakol, and A. Tworkowski, ibid. 332, 339 (1998); E. Covas and R. Tavakol, Phys. Rev. E 60, 5435 (1999); M. Küker, R. Arlt, and G. Rd̈iger, Astron. Astrophys. 343, 977 (1999); M. A. J. H. Ossendrijver, ibid. 359, 364 (2000).
64. S. Schmalz and M. Stix, Astron. Astrophys. 245, 654 (1991); F. Feudel, W. Jansen, and J. Kurths, Int. J. Bifurcation Chaos Appl. Sci. Eng. 3, 131 (1993); M. A. J. H. Ossendrijver, P. Hoyng, and D. Schmitt, Astron. Astrophys. 313, 938 (1996); D. Schmitt, M. Schüssler, and A. Ferriz-Mas, ibid. 311, L1 (1996); J. M. Brooke, J. Pelt, R. Tavakol, and A. Tworkowski, ibid. 332, 339 (1998); E. Covas and R. Tavakol, Phys. Rev. E 60, 5435 (1999); M. Küker, R. Arlt, and G. Rd̈iger, Astron. Astrophys. 343, 977 (1999); M. A. J. H. Ossendrijver, ibid. 359, 364 (2000).
65. S. Schmalz and M. Stix, Astron. Astrophys. 245, 654 (1991); F. Feudel, W. Jansen, and J. Kurths, Int. J. Bifurcation Chaos Appl. Sci. Eng. 3, 131 (1993); M. A. J. H. Ossendrijver, P. Hoyng, and D. Schmitt, Astron. Astrophys. 313, 938 (1996); D. Schmitt, M. Schüssler, and A. Ferriz-Mas, ibid. 311, L1 (1996); J. M. Brooke, J. Pelt, R. Tavakol, and A. Tworkowski, ibid. 332, 339 (1998); E. Covas and R. Tavakol, Phys. Rev. E 60, 5435 (1999); M. Küker, R. Arlt, and G. Rd̈iger, Astron. Astrophys. 343, 977 (1999); M. A. J. H. Ossendrijver, ibid. 359, 364 (2000).
66. S. Schmalz and M. Stix, Astron. Astrophys. 245, 654 (1991); F. Feudel, W. Jansen, and J. Kurths, Int. J. Bifurcation Chaos Appl. Sci. Eng. 3, 131 (1993); M. A. J. H. Ossendrijver, P. Hoyng, and D. Schmitt, Astron. Astrophys. 313, 938 (1996); D. Schmitt, M. Schüssler, and A. Ferriz-Mas, ibid. 311, L1 (1996); J. M. Brooke, J. Pelt, R. Tavakol, and A. Tworkowski, ibid. 332, 339 (1998); E. Covas and R. Tavakol, Phys. Rev. E 60, 5435 (1999); M. Küker, R. Arlt, and G. Rd̈iger, Astron. Astrophys. 343, 977 (1999); M. A. J. H. Ossendrijver, ibid. 359, 364 (2000).
67. S. Schmalz and M. Stix, Astron. Astrophys. 245, 654 (1991); F. Feudel, W. Jansen, and J. Kurths, Int. J. Bifurcation Chaos Appl. Sci. Eng. 3, 131 (1993); M. A. J. H. Ossendrijver, P. Hoyng, and D. Schmitt, Astron. Astrophys. 313, 938 (1996); D. Schmitt, M. Schüssler, and A. Ferriz-Mas, ibid. 311, L1 (1996); J. M. Brooke, J. Pelt, R. Tavakol, and A. Tworkowski, ibid. 332, 339 (1998); E. Covas and R. Tavakol, Phys. Rev. E 60, 5435 (1999); M. Küker, R. Arlt, and G. Rd̈iger, Astron. Astrophys. 343, 977 (1999); M. A. J. H. Ossendrijver, ibid. 359, 364 (2000).
68. S. Schmalz and M. Stix, Astron. Astrophys. 245, 654 (1991); F. Feudel, W. Jansen, and J. Kurths, Int. J. Bifurcation Chaos Appl. Sci. Eng. 3, 131 (1993); M. A. J. H. Ossendrijver, P. Hoyng, and D. Schmitt, Astron. Astrophys. 313, 938 (1996); D. Schmitt, M. Schüssler, and A. Ferriz-Mas, ibid. 311, L1 (1996); J. M. Brooke, J. Pelt, R. Tavakol, and A. Tworkowski, ibid. 332, 339 (1998); E. Covas and R. Tavakol, Phys. Rev. E 60, 5435 (1999); M. Küker, R. Arlt, and G. Rd̈iger, Astron. Astrophys. 343, 977 (1999); M. A. J. H. Ossendrijver, ibid. 359, 364 (2000).