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Long-term observations show that blazar object S5 0716 +714 has complicated behavious on multiband. In this paper, the light curves in the radio, V-band and X-ray bands of four outbursts are studied by the chaos theory. We calculate their correlation dimensions and Lyapunov exponents and find that 1) these two values are in a range between a stochastic system and a pure chaotic system; 2) the phase locus of S5 0716 +714 is a chaotic system similar to the Rossler attractor. Various internal or external factors may produce noises, resulting in the fact that the correlation dimension and Lyapunov exponent may be higher than those of the Rossler attractor and the phase locus might be orderless. According to our analysis, we conclude that the light curves of S5 0714+716 show some chaotic features and the variability of this source may be a chaotic phenomenon.
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Keywords:
- blazar /
- light curves /
- chaotic characteristics /
- S5 0716+714
[1] Urry C M, Padovani P 1995 Pub. Astron. Soc. Pac. 107 803
[2] Zhang X, Xie G Z, Bai J M 1998 Astron. Astrophys. 330 469
[3] Sillanpaa A, Haarala S, Valtonen M J, Sundelius B, Byrd G G 1988 Astrophys. J. 325 628
[4] Zhang H J, Zhang X, Dong F T, Zheng Y G, Tang L, Mao L S 2009 Acta Astron. Sin. 50 141 (in Chinese) [张皓晶, 张雄, 董富通, 郑永刚, 唐玲, 毛李胜 2009 天文学报 50 141]
[5] Zhang H J, Zhang X 2007 Acta Phys. Sin. 56 4305 (in Chinese) [张皓晶, 张雄 2007 56 4305]
[6] Zhang H J, Zhao G, Zhang X, Dong F T, Xie Z H, Yi T F, Zheng Y G, Bao Y Y 2009 Sci. Sin. Phys. G 39 1029 (in Chinese) [张皓晶, 赵刚, 张雄, 董富通, 谢照华, 易庭丰, 郑永刚, 鲍玉英 2009 中国科学 G 39 1029]
[7] Tang J, Fu M X, Wu X B 2012 Acta Phys. Sin. 61 219501 (in Chinese) [唐洁, 傅明星, 吴学兵 2012 61 219501]
[8] Tang J, Wu X B 2011 Acta Phys. Sin. 60 119801 (in Chinese) [唐洁, 吴学兵 2011 60 119801]
[9] Xiong D, Zhang H, Zhang X, Zheng Y, Liu W, Mao L, Huang B, Kang T, Cha Y, Guo F 2013 Astrophys. Spa. Sci. 343 345
[10] Dettmann C P, Frankel N E, Cornish N J 1994 Phys. Rev. D 50 R618
[11] Dettmann C P, Frankel N E, Cornish N J 1995 Fractal 3 161
[12] de Moura A P S, Letelier P S 2000 Phys. Rev. E 61 6506
[13] Caranicolas N D, Zotos E E 2010 Astron. Nachrichten. 331 330
[14] Timmer J, Schwarz U, Voss H U, Wardinski I, Belloni T, Hasinger G, Klis M, Kurths J 2000 Phys. Rev. E 61 1342
[15] Maccarone T J 2002 Mon. Not. R. Astron. Soc. 336 1371
[16] Emmanoulopulos D 2007 Ph. D. Dissertation (Heidelberg: Ruperto-Carola University of Heidelberg)
[17] Li T B 2006 Physics 35 367 (in Chinese) [李惕碚 2006 物理 35 367]
[18] Dong S Z, Zhou H, Wu Y F, Chang P, Xu A T, Li H Z 2012 J. Yunnan Normal Univ. 32 20 (in Chinese) [董诗忠, 周宏, 吴永凤, 常平, 徐安田, 李怀珍 2012 云南师范大学学报 32 20]
[19] Misra R, Harikrishnan K P, Ambika G, Kembhavi A K 2006 Astrophys. J. 643 1114
[20] Packard N H, Crutchfield J P, Farmer J D, Shaw R S 1980 Phys. Rev. Lett. 45 712
[21] Harikrishnan K P, Misra R,Ambika G, Kembhavi A K 2006 Physica D 215 137
[22] Liu S D, Liang F M, Liu S S, Xin G J 2003 Chaos and Fractal in Natural Sciences (Beijing: Peking University Press) p35 (in Chinese) [刘式达, 梁福明, 刘式适, 辛国君 2003 自然科学中的混沌和分形 (北京: 北京大学出版社) 第35页]
[23] Cornish N J, Levin J 2003 Class. Quant. Grav. 20 1649
[24] Raiteri C M, Villata M, Tosti G 2003 Astron. Astrophys. 402 151
[25] Venturi T, Dallacasa D, Orfei A, Bondi M, Fanti R, Gregorini L, Mantovani F, Stanghellini C, Trigilio C, Umana G 2001 Astron. Astrophys. 379 755
[26] Donato D, Sambruna R M, Gliozzi M 2005 Astron. Astrophys. 433 1163
[27] Ferrero E, Wagner S J, Emmanoulopoulos D, Ostorero L 2006 Astron. Astrophys. 457 133
[28] Wallinder F H, Kato S, Abramowicz M A 1992 Astron. Astrophys. Rev. 4 79
[29] Winters W F, Balbus S A, Hawley J F 2003 Mon. Not. R. Astron. Soc. 340 519
[30] Mukhopadhyay B 2009 Astrophys. J. 694 387
[31] Zhang J, Liang E W, Zhang S N, Bai J M 2012 Astrophys. J. 752 157
[32] Zhang J, Zhang S N, Liang E W 2013 Astrophys. J. 767 8
-
[1] Urry C M, Padovani P 1995 Pub. Astron. Soc. Pac. 107 803
[2] Zhang X, Xie G Z, Bai J M 1998 Astron. Astrophys. 330 469
[3] Sillanpaa A, Haarala S, Valtonen M J, Sundelius B, Byrd G G 1988 Astrophys. J. 325 628
[4] Zhang H J, Zhang X, Dong F T, Zheng Y G, Tang L, Mao L S 2009 Acta Astron. Sin. 50 141 (in Chinese) [张皓晶, 张雄, 董富通, 郑永刚, 唐玲, 毛李胜 2009 天文学报 50 141]
[5] Zhang H J, Zhang X 2007 Acta Phys. Sin. 56 4305 (in Chinese) [张皓晶, 张雄 2007 56 4305]
[6] Zhang H J, Zhao G, Zhang X, Dong F T, Xie Z H, Yi T F, Zheng Y G, Bao Y Y 2009 Sci. Sin. Phys. G 39 1029 (in Chinese) [张皓晶, 赵刚, 张雄, 董富通, 谢照华, 易庭丰, 郑永刚, 鲍玉英 2009 中国科学 G 39 1029]
[7] Tang J, Fu M X, Wu X B 2012 Acta Phys. Sin. 61 219501 (in Chinese) [唐洁, 傅明星, 吴学兵 2012 61 219501]
[8] Tang J, Wu X B 2011 Acta Phys. Sin. 60 119801 (in Chinese) [唐洁, 吴学兵 2011 60 119801]
[9] Xiong D, Zhang H, Zhang X, Zheng Y, Liu W, Mao L, Huang B, Kang T, Cha Y, Guo F 2013 Astrophys. Spa. Sci. 343 345
[10] Dettmann C P, Frankel N E, Cornish N J 1994 Phys. Rev. D 50 R618
[11] Dettmann C P, Frankel N E, Cornish N J 1995 Fractal 3 161
[12] de Moura A P S, Letelier P S 2000 Phys. Rev. E 61 6506
[13] Caranicolas N D, Zotos E E 2010 Astron. Nachrichten. 331 330
[14] Timmer J, Schwarz U, Voss H U, Wardinski I, Belloni T, Hasinger G, Klis M, Kurths J 2000 Phys. Rev. E 61 1342
[15] Maccarone T J 2002 Mon. Not. R. Astron. Soc. 336 1371
[16] Emmanoulopulos D 2007 Ph. D. Dissertation (Heidelberg: Ruperto-Carola University of Heidelberg)
[17] Li T B 2006 Physics 35 367 (in Chinese) [李惕碚 2006 物理 35 367]
[18] Dong S Z, Zhou H, Wu Y F, Chang P, Xu A T, Li H Z 2012 J. Yunnan Normal Univ. 32 20 (in Chinese) [董诗忠, 周宏, 吴永凤, 常平, 徐安田, 李怀珍 2012 云南师范大学学报 32 20]
[19] Misra R, Harikrishnan K P, Ambika G, Kembhavi A K 2006 Astrophys. J. 643 1114
[20] Packard N H, Crutchfield J P, Farmer J D, Shaw R S 1980 Phys. Rev. Lett. 45 712
[21] Harikrishnan K P, Misra R,Ambika G, Kembhavi A K 2006 Physica D 215 137
[22] Liu S D, Liang F M, Liu S S, Xin G J 2003 Chaos and Fractal in Natural Sciences (Beijing: Peking University Press) p35 (in Chinese) [刘式达, 梁福明, 刘式适, 辛国君 2003 自然科学中的混沌和分形 (北京: 北京大学出版社) 第35页]
[23] Cornish N J, Levin J 2003 Class. Quant. Grav. 20 1649
[24] Raiteri C M, Villata M, Tosti G 2003 Astron. Astrophys. 402 151
[25] Venturi T, Dallacasa D, Orfei A, Bondi M, Fanti R, Gregorini L, Mantovani F, Stanghellini C, Trigilio C, Umana G 2001 Astron. Astrophys. 379 755
[26] Donato D, Sambruna R M, Gliozzi M 2005 Astron. Astrophys. 433 1163
[27] Ferrero E, Wagner S J, Emmanoulopoulos D, Ostorero L 2006 Astron. Astrophys. 457 133
[28] Wallinder F H, Kato S, Abramowicz M A 1992 Astron. Astrophys. Rev. 4 79
[29] Winters W F, Balbus S A, Hawley J F 2003 Mon. Not. R. Astron. Soc. 340 519
[30] Mukhopadhyay B 2009 Astrophys. J. 694 387
[31] Zhang J, Liang E W, Zhang S N, Bai J M 2012 Astrophys. J. 752 157
[32] Zhang J, Zhang S N, Liang E W 2013 Astrophys. J. 767 8
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