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Complex network theory is used to characterize the temporal and phase space features of a time series when it is transferred into a network. In this paper, we study the motif ranks of complex networks induced from different categories of time series with periodic bifurcations and chaos, which are generated with two algorithms: the Visiblity Graph (VG) algorithm and the Phase-space Reconstruction (PR) algorithm. The advantages of both algorithms are analyzed.
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Keywords:
- time series /
- network motif /
- chaos /
- periodic bifurcation
[1] [1]Albert R, Barabasi A L 2002 Rev. Mod. Phys. 74 47
[2] [2]Newman M E J 2003 SIAM REV 45 167
[3] [3]Wang X F,Li X,Chen G R 2006 Complex Network Theroy And Application p1(in Chinese)[汪小帆、李翔、陈关荣 2006 复杂网络理论及其应用(北京:清华大学出版社) 第1页 ]
[4] [4]Wu J S, Di Z R 2004 Progress In Physics 24 18 (in Chinese)[吴金闪、狄增如 2004 物理学进展 24 18]
[5] [5]Zhou T, Bo W H, Wang B H 2005 Physics 34 31 (in Chinese)[周涛、柏文浩、汪秉宏 2005 物理 34 31]
[6] [6]Fang J Q 2007 Progress in Natural Science 17 841 (in Chinese)[方锦清 2007 自然科学进展 17841]
[7] [7]Pei W D, Liu Z X, Chen Z Q, Yuan Z Z, 2008 Acta Phys. Sin. 57 6777 (in Chinese)[裴伟东、刘忠信、陈增强、袁著祉 2008 物理学报 57 6777]
[8] [8]Wang G Z, Cao Y J, Bao Z J, Han Z X 2009 Acta Phys. Sin. 58 3597 (in Chinese)[王光增、曹一家、包哲静、韩祯祥2009物理学报58 3597]
[9] [9]Zhang J, Small M 2006 Phys. Rev. Lett. 96 238701
[10] ]Lucasa L, Luque B, Bllesteros F, Luque J, Nuno J C 2008 Proc. Natl. Acad. Scai 105 4972
[11] ]Xu X K, Zhang J, Small M 2008 Proc. Natl. Acad. Scai 105 50
[12] ]Zhang J, Sun J F, Luo X D, Zhang K, Tomomichi Nakamura, Small M Physica D 237 2856
[13] ]Lucasa L, Luuque B, Luque J, Nuno J C 2009 Europhysics Letters 86 30001
[14] ]Yang Z A, Chen S G, Wang G R 1996 Acta Phys. Sin. 45 904 (in Chinese)[杨志安、陈式刚、王光瑞 1996 物理学报45 904]
[15] ]Liu B Z 1995 Nonlinear Dynamics and Chaotic Basis (Changchun:Dongbei Normal University Press)p174 (in Chinese)[刘秉正 1995 非线性动力学与混沌基础(修订本)(东北:东北师范大学出版社)第174页]
[16] ]Milo R, Shen orr R, Itzkovitz S, Kashan N, Chklovskii D, Alon U 2002 Science 298 824
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[1] [1]Albert R, Barabasi A L 2002 Rev. Mod. Phys. 74 47
[2] [2]Newman M E J 2003 SIAM REV 45 167
[3] [3]Wang X F,Li X,Chen G R 2006 Complex Network Theroy And Application p1(in Chinese)[汪小帆、李翔、陈关荣 2006 复杂网络理论及其应用(北京:清华大学出版社) 第1页 ]
[4] [4]Wu J S, Di Z R 2004 Progress In Physics 24 18 (in Chinese)[吴金闪、狄增如 2004 物理学进展 24 18]
[5] [5]Zhou T, Bo W H, Wang B H 2005 Physics 34 31 (in Chinese)[周涛、柏文浩、汪秉宏 2005 物理 34 31]
[6] [6]Fang J Q 2007 Progress in Natural Science 17 841 (in Chinese)[方锦清 2007 自然科学进展 17841]
[7] [7]Pei W D, Liu Z X, Chen Z Q, Yuan Z Z, 2008 Acta Phys. Sin. 57 6777 (in Chinese)[裴伟东、刘忠信、陈增强、袁著祉 2008 物理学报 57 6777]
[8] [8]Wang G Z, Cao Y J, Bao Z J, Han Z X 2009 Acta Phys. Sin. 58 3597 (in Chinese)[王光增、曹一家、包哲静、韩祯祥2009物理学报58 3597]
[9] [9]Zhang J, Small M 2006 Phys. Rev. Lett. 96 238701
[10] ]Lucasa L, Luque B, Bllesteros F, Luque J, Nuno J C 2008 Proc. Natl. Acad. Scai 105 4972
[11] ]Xu X K, Zhang J, Small M 2008 Proc. Natl. Acad. Scai 105 50
[12] ]Zhang J, Sun J F, Luo X D, Zhang K, Tomomichi Nakamura, Small M Physica D 237 2856
[13] ]Lucasa L, Luuque B, Luque J, Nuno J C 2009 Europhysics Letters 86 30001
[14] ]Yang Z A, Chen S G, Wang G R 1996 Acta Phys. Sin. 45 904 (in Chinese)[杨志安、陈式刚、王光瑞 1996 物理学报45 904]
[15] ]Liu B Z 1995 Nonlinear Dynamics and Chaotic Basis (Changchun:Dongbei Normal University Press)p174 (in Chinese)[刘秉正 1995 非线性动力学与混沌基础(修订本)(东北:东北师范大学出版社)第174页]
[16] ]Milo R, Shen orr R, Itzkovitz S, Kashan N, Chklovskii D, Alon U 2002 Science 298 824
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