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The radio fluxes of the quasars 3C 345, 3C 279 and 3C 273 at a frequency of 8.0 GHz were collected in a time period from 1965 to 2012 based on the database of University of Michigan Radio Astronomy Observatory. The time series of the quasar variability is decomposed into trend components, periodic components and high frequency components by the ensemble empirical mode decomposition. Then chaotic characteristic quantities of the high frequency component is analyzed, that is, saturation correlation dimension, maximum Lyapunov exponent and Kolmogorov entropy. The results show that the variability of quasars has the chaotic characteristic as well as the characteristic of periodicity. The variability of quasars is due to the comprehensive consequence of a physical mechanism of the periodic phenomenon combined with the nonlinear mechanism of the chaos phenomenon.
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Keywords:
- quasar /
- period /
- ensemble empirical mode decomposition /
- chaos
[1] Abramowicz M A, Nobili L 1982 Nature 300 506
[2] Fan J H, Liu Y, Yuan Y H 2007 Astron. Astrophys. 462 547
[3] Zhang H J, Zhao G, Zhang X, Bai J M 2010 Sci. China G 53 252
[4] Bai J M, Lee M G 2003 Astrophys. J. 585L 113
[5] Tang J, Zhang X 2010 Acta Phys. Sin. 59 7516 (in Chinese) [唐洁, 张雄 2010 59 7516]
[6] Valtonen M, Kidger M, Lehto H, Poyner G 2008 Astron. Astrophys. 477 407
[7] Tang J 2012 Acta Astron. Sin. 53 1 (in Chinese) [唐洁 2012 天文学报 53 1]
[8] Huang N E, Shen Z, Long S R 1998 Proc. Roy. Soc. London A 454 903
[9] Zhao H W, Huang N E 2004 Proc. Roy. Soc. London A 460 1597
[10] Liu D Y, Wang Y W, Wang X, He K, Zhang X J, Yang C X 2012 Acta Phys. Sin. 61 150506 (in Chinese) [刘丹阳, 王亚伟, 王仙, 何昆, 张兴娟, 杨春信 2012 61 150506]
[11] L J H, Lu J A, Chen S H 2001 Analysis and Application of Chaotic Time Series (Wuhan: Wuhan University Press) p57 (in Chinese) [吕金虎, 陆君安, 陈士华 2001 混沌时间序列分析及其应用 (武汉: 武汉大学出版社) 第57页]
[12] Takens F 1981 Dynamical System and Turbulence, Lecture Notes in Mathematics (Berlin: Springer) p366
[13] Packard N H, Crutchfield J P, Farmer J D, Shaw R S 1980 Phys. Rev. Lett. 45 712
[14] Fraser A M, Swinney H L 1986 Phys. Rev. A 33 1134
[15] Grassberger P, Procaccia I 1983 Physica D 9 189
[16] Wolf A, Swift J B, Swinney H L, Vastno J A 1985 Physi-ca D 16 285
[17] Tang J 2013 Acta Phys. Sin. 62 129701 (in Chinese) [唐洁 2013 62 129701]
[18] Fan J H, Romero G E, Lin R G 2001 Chin. Astron. Astrophys. 25 282
[19] Fan J H 1999 Mon. Not. R. Astron. Soc. 308 1032
[20] Tang J, Zhang X 2012 Acta Phys. Sin. 61 169601 (in Chinese) [唐洁, 张雄 2012 61 169601]
[21] Varvoglis H, Papadopoulo S K 1983 Astrophys. J. 270 L95
[22] Sillanpää A, Haarala S, Valtonen M J, Sundelius B, Byrd G G 1988 Astrophys. J. 325 628
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[1] Abramowicz M A, Nobili L 1982 Nature 300 506
[2] Fan J H, Liu Y, Yuan Y H 2007 Astron. Astrophys. 462 547
[3] Zhang H J, Zhao G, Zhang X, Bai J M 2010 Sci. China G 53 252
[4] Bai J M, Lee M G 2003 Astrophys. J. 585L 113
[5] Tang J, Zhang X 2010 Acta Phys. Sin. 59 7516 (in Chinese) [唐洁, 张雄 2010 59 7516]
[6] Valtonen M, Kidger M, Lehto H, Poyner G 2008 Astron. Astrophys. 477 407
[7] Tang J 2012 Acta Astron. Sin. 53 1 (in Chinese) [唐洁 2012 天文学报 53 1]
[8] Huang N E, Shen Z, Long S R 1998 Proc. Roy. Soc. London A 454 903
[9] Zhao H W, Huang N E 2004 Proc. Roy. Soc. London A 460 1597
[10] Liu D Y, Wang Y W, Wang X, He K, Zhang X J, Yang C X 2012 Acta Phys. Sin. 61 150506 (in Chinese) [刘丹阳, 王亚伟, 王仙, 何昆, 张兴娟, 杨春信 2012 61 150506]
[11] L J H, Lu J A, Chen S H 2001 Analysis and Application of Chaotic Time Series (Wuhan: Wuhan University Press) p57 (in Chinese) [吕金虎, 陆君安, 陈士华 2001 混沌时间序列分析及其应用 (武汉: 武汉大学出版社) 第57页]
[12] Takens F 1981 Dynamical System and Turbulence, Lecture Notes in Mathematics (Berlin: Springer) p366
[13] Packard N H, Crutchfield J P, Farmer J D, Shaw R S 1980 Phys. Rev. Lett. 45 712
[14] Fraser A M, Swinney H L 1986 Phys. Rev. A 33 1134
[15] Grassberger P, Procaccia I 1983 Physica D 9 189
[16] Wolf A, Swift J B, Swinney H L, Vastno J A 1985 Physi-ca D 16 285
[17] Tang J 2013 Acta Phys. Sin. 62 129701 (in Chinese) [唐洁 2013 62 129701]
[18] Fan J H, Romero G E, Lin R G 2001 Chin. Astron. Astrophys. 25 282
[19] Fan J H 1999 Mon. Not. R. Astron. Soc. 308 1032
[20] Tang J, Zhang X 2012 Acta Phys. Sin. 61 169601 (in Chinese) [唐洁, 张雄 2012 61 169601]
[21] Varvoglis H, Papadopoulo S K 1983 Astrophys. J. 270 L95
[22] Sillanpää A, Haarala S, Valtonen M J, Sundelius B, Byrd G G 1988 Astrophys. J. 325 628
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