Abstract
We present a simplified model cycle, using the available data, for the monthly sunspot numbers random variables {X t } t = 1 133, where 133 is taken as the mean duration of the Schwabe’s cycle. We present a fit for the mean and standard deviation of X t . In the descending and ascending phases, we analyse the probability histogram of the monthly sunspot numbers fluctuations.
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References
Babcock, H.W.: The topology of the sun’s magnetic field and the 22-year cycle. Astrophys. J. 133(2), 572–587 (1961)
Bak, P., Tang, C., Wiesenfeld, K.: Self-organized criticality. Phys. Rev. Lett. A38, 364–374 (1988)
Bramwell, S.T., Christensen, K., Fortin, J.Y., Holdsworth, P.C.W., Jensen, H.J., Lise, S., López, J.M., Nicodemi, M., Sellitto, M.: Universal fluctuations in correlated systems. Phys. Rev. Lett. 84, 3744–3747 (2000)
Bramwell, S.T., Fortin, J.Y., Holdsworth, P.C.W., Peysson, S., Pinton, J.F., Portelli, B., Sellitto, M.: Magnetic Fluctuations in the classical XY model: the origin of an exponential tail in a complex system. Phys. Rev. E 63, 041106 (2001)
Bramwell, S.T., Holdsworth, P.C.W., Pinton, J.F.: Universality of rare fluctuations in turbulence and critical phenomena. Nature 396, 552–554 (1998)
Dahlstedt, K., Jensen, H.J.: Fluctuation spectrum and size scaling of river flow and level. Phys. A 348, 596–610 (2005)
Dahlstedt, K., Jensen, H.J.: Universal fluctuations and extreme-value statistics. J. Phys. A Math. Gen. 34, 11193–11200 (2001)
Gonçalves, R., Ferreira, H., Stollenwerk, N., Pinto, A.A.: Universal fluctuations of AEX index. Phys. A (to appear)
Gonçalves, R., Ferreira, H., Pinto, A.A., Stollenwerk, N.: Universality in nonlinear prediction of complex systems. J. Dif. Equ. Appl. 15, 1067–1076 (2009)
Gonçalves, R., Ferreira, H., Pinto, A.A., Stollenwerk, N.: Universality in the Stock Exchange Market. J. Dif. Equ. Appl. (to appear)
Gonçalves, R., Ferreira, H., Pinto, A.A.: Universality in energy sources. (submitted)
Gonçalves, R., Ferreira, H., Pinto, A.A.: Universal fluctuations of the Dow Jones. (submitted)
Gonçalves, R., Ferreira, H., Pinto, A.A.: A qualitative and quantitative Econophysics stock market model (submitted)
Gonçalves, R., Pinto, A.A.: BHP universality and gaussianity in sunspot numbers fluctuations. arXiv:0802.2880 4 physics.data-an (2008)
Gonçalves, R., Pinto, A.A.: Negro and Danube are mirror rivers. J. Dif. Equ. Appl. (to appear)
Gonçalves, R., Pinto, A.A., Calheiros, F.: Nonlinear prediction in riverflow – the Paiva river case. In: Staicu, V. (eds.) Differential Equations Chaos and Variational Problems. Series: Progress in Nonlinear Differential Equations and Their Applications, vol. 75, pp. 231–240. Birkhauser Verlag, Basel (2007)
Gonçalves, R., Pinto, A.A., Calheiros, F.: Comparison of methodologies in river flow prediction. The Paiva river case. In: Tas, K. et al. (eds.) Mathematical Methods in Engineering, pp. 381–390. Springer, Heidelberg (2007)
Gonçalves, R., Pinto, A.A., Stollenwerk, N.: Cycles and universality in sunspot numbers fluctuations. Astrophys. J. 691, 1583–1586 (2009)
Lu, E., Hamilton, R.: Avalanches and distributions of solar flares. Astrophys. J. 380, L89–L92 (1991)
McNish, A.G., Lincoln, J.V.: Prediction of sunspot numbers, Trans. Am. Geophys. 30, 673–685 (1949)
van Milligen, B.Ph., Sánchez, R., Carreras, B.A., Lynch, V.E., LaBombard, B., Pedrosa, M.A., Hidalgo, C., Gonçalves, B., Balbín, R., The Team, W7-AS.: Additional evidence for the universality of the probability distribution of turbulent fluctuations and fluxes in the scrape-off layer region of fusion plasmas. Phys. Plasmas 12, 05207-1-05207-7 (2005)
Palu\check{s}, M., Novotná, D.: Sunspot cycle, a nonlinear oscillator?, Phys. Rev. Lett. 83(17), 3406–3409 (1999)
Pinto, A.A.: Game Theory and Duopoly Models. Interdisciplinary Applied Mathematics Series. Springer (to appear)
Pinto, A.A., Rand, D.A., Ferreira, F.: Fine Structures of Hyperbolic Diffeomorphisms. Springer-Verlag Monograph (2010)
Rabin, D., Wilson, R., Moore, R.: Bimodality of the solar cycle. Geophys. Res. Lett. 13, 352–354 (1986)
Schwabe, H.: Die Sohne. Astron. Nachr. 20, 283–286 (1843)
Sinha-Ray, P., Borda de Água, L., Jensen, H.J.: Threshold dynamics, multifractality and universal fluctuations in the SOC forest fire: facets of an auto-ignition model. Phys. D 157, 186–196 (2001)
Acknowledgements
We thank Nico Stollenwerk, in particular, for showing us the relevance of the BHP distribution. We would like to thank Robert Wilson for giving us very useful information on the sunspot numbers. We thank LIAAD-INESC Porto LA, Calouste Gulbenkian Foundation, PRODYN-ESF, POCTI and POSI by FCT and Ministério da Ciência e da Tecnologia, and the FCT Pluriannual Funding Program of the LIAAD-INESC Porto LA and of the Research Center of Mathematics of the University of Minho, for their financial support.
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Gonçalves, R., Pinto, A.A. (2011). A Stochastic Model for Wolf’s Sunspot Number. In: Peixoto, M., Pinto, A., Rand, D. (eds) Dynamics, Games and Science II. Springer Proceedings in Mathematics, vol 2. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14788-3_30
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DOI: https://doi.org/10.1007/978-3-642-14788-3_30
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