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We propose an improved visibility graph method, i.e., limited penetrable visibility graph, for establishing complex network from time series. Through evaluating the degree distributions of three visibility algorithms(visibility graph, horizontal visibility graph, limited penetrable visibility graph), we find that the horizontal visibility graph cannot distinguish signals from periodic, fractal, and chaotic systems; for fractal signal, the degree distributions obtained from visibility graph and limited penetrable visibility both can be well fitted to a power-law(scale-free distribution), but the anti-noise ability is not good; for periodic and chaotic signals, the limited penetrable visibility graph shows better anti-noise ability than visibility graph. In this regard, we use the limited penetrable visibility graph to extract the network degree distribution parameters from conductance fluctuating signals measured from oil-gas-water three-phase flow test. The results indicate that combination parameters of network degree distribution can be used to classify typical three phase flow patterns, e.g., oil-in-water bubble flow, bubble-slug transitional flow and slug flow.
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Keywords:
- complex network /
- statistical characteristics /
- limited penetrable visibility graph /
- model evaluation
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[2] Barabási A L, Albert R 1999 Science 286 509
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[5] Wang W X, Wang B H, Hu B, Yan G, Ou Q 2005 Phys. Rev. Lett. 94 188702
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[9] Zhang J, Small M 2006 Phys. Rev. Lett. 96 238701
[10] Zhang J, Sun J F, Luo S D, Zhang K, Nakamura T, Small M 2008 Physica D 237 2856
[11] Marwan N, Donges J F, Zou Y, Donner R V, Kurths J 2009 Phys. Lett. A 373 4246
[12] Donner R V, Zou Y, Donges J F, Marwan N, Kurths J 2010 New J. Phys. 12 033025
[13] Zhang J, Zhang K, Feng J F, Small M 2010 PLoS Comput. Biol. 6 e1001033
[14] Qian M C, Jiang Z Q, Zhou W X 2010 J. Phys. A 33 335002
[15] Yang Y, Yang H J 2008 Physica A 387 1381
[16] Lacasa L, Luque B, Ballesteros F, Luque J, Nuno J C 2008 Proc. Natl. Acad. Sci. USA 105 4972
[17] Lacasa L, Luque B, Luque J, Nuno J C 2009 Europhys. Lett. 86 30001
[18] Lacasa L, Toral R 2010 Phys. Rev. E 82 036120
[19] Yang Y, Wang J B, Yang H J 2009 Physica A 388 20
[20] Elsner J B, Jagger T H, Fogarty E A 2009 Geophys. Res. Lett. 36 16
[21] Liu C, Zhou W, Yuan W 2010 Physica A 389 2675
[22] Shao Z G 2010 Appl. Phys. Lett. 96 073703
[23] Dong Z, Li X 2009 Acta Phys. Sin. 59 1600(in Chinese)[董昭, 李翔 2009 59 1600]
[24] Luque B, Lacasa L, Ballesteros F, Luque L 2009 Phys. Rev. E 80 046103
[25] Xu X, Zhang J, Small M 2008 Proc. Natl. Acad. Sci. USA 105 19601
[26] Chavez M, Valencia M, Navarro V, Latora V, Martinerie J 2010 Phys. Rev. Lett. 104 18701
[27] Gao Z K, Jin N D 2009 Phys. Rev. E 79 066303
[28] Gao Z K, Jin N D 2009 Chaos 19 033137
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[1] Watts D J, Strogatz S H 1998 Nature 393 440
[2] Barabási A L, Albert R 1999 Science 286 509
[3] Albert R, Barabási A L 2002 Rev. Mod. Phys. 174 47
[4] Newman M E J 2003 SIAM Rev. 45 167
[5] Wang W X, Wang B H, Hu B, Yan G, Ou Q 2005 Phys. Rev. Lett. 94 188702
[6] Boccaletti S, Latora V, Moreno Y, Chavez M, Hwang D U 2006 Phys. Rep. 424 175
[7] Huang L, Park K, Lai Y C, Yang L, Yang K Q 2006 Phys. Rev. Lett. 97 164101
[8] Barabási A L 2009 Science 325 412
[9] Zhang J, Small M 2006 Phys. Rev. Lett. 96 238701
[10] Zhang J, Sun J F, Luo S D, Zhang K, Nakamura T, Small M 2008 Physica D 237 2856
[11] Marwan N, Donges J F, Zou Y, Donner R V, Kurths J 2009 Phys. Lett. A 373 4246
[12] Donner R V, Zou Y, Donges J F, Marwan N, Kurths J 2010 New J. Phys. 12 033025
[13] Zhang J, Zhang K, Feng J F, Small M 2010 PLoS Comput. Biol. 6 e1001033
[14] Qian M C, Jiang Z Q, Zhou W X 2010 J. Phys. A 33 335002
[15] Yang Y, Yang H J 2008 Physica A 387 1381
[16] Lacasa L, Luque B, Ballesteros F, Luque J, Nuno J C 2008 Proc. Natl. Acad. Sci. USA 105 4972
[17] Lacasa L, Luque B, Luque J, Nuno J C 2009 Europhys. Lett. 86 30001
[18] Lacasa L, Toral R 2010 Phys. Rev. E 82 036120
[19] Yang Y, Wang J B, Yang H J 2009 Physica A 388 20
[20] Elsner J B, Jagger T H, Fogarty E A 2009 Geophys. Res. Lett. 36 16
[21] Liu C, Zhou W, Yuan W 2010 Physica A 389 2675
[22] Shao Z G 2010 Appl. Phys. Lett. 96 073703
[23] Dong Z, Li X 2009 Acta Phys. Sin. 59 1600(in Chinese)[董昭, 李翔 2009 59 1600]
[24] Luque B, Lacasa L, Ballesteros F, Luque L 2009 Phys. Rev. E 80 046103
[25] Xu X, Zhang J, Small M 2008 Proc. Natl. Acad. Sci. USA 105 19601
[26] Chavez M, Valencia M, Navarro V, Latora V, Martinerie J 2010 Phys. Rev. Lett. 104 18701
[27] Gao Z K, Jin N D 2009 Phys. Rev. E 79 066303
[28] Gao Z K, Jin N D 2009 Chaos 19 033137
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