Complex system reconstruction

Zhang Hai-Feng; Wang Wen-Xu

doi:10.7498/aps.69.20200001

Abstract

Open complex systems far from equilibrium widely exist in the nature and the fields of society and technology, which are the main research objects of complexity science. Through the exchange of energy and material with the outside world, complex systems can form a variety of internal structures, orders and laws by self-organization behaviors, which poses an arduous challenge to the understanding and predicting complex systems. With the improvement of experimental technology and the progress of science and technology, the data reflecting the mechanism of various complex systems are increasing exponentially, thereby providing new opportunities for studying complex systems. Revealing the structures and dynamics of complex systems from the measured data is an inverse problem in the field of physics, which is the premise of understanding complex systems, predicting the evolution of system state, and regulating system state. However, it is very difficult to solve this inverse problem due to the diversity and complexity of complex system. Therefore, we need to fully mine the hidden knowledge and deep mechanism in the data with the help of interdisciplinary integration. In this paper we briefly review the research results of complex system in recent years, especially the reconstruction of complex network structures, hoping to inspire the innovation to the inverse problem of complex systems. Meanwhile, we hope that researchers in different fields can pay much attention to the inverse problems of complex systems, promote the cross and integration of nature, society, economy, biology and technology, and solve the scientific problems that we are facing.

Keywords:

Authors and contacts

Zhang Hai-Feng¹,
Wang Wen-Xu²

1.
School of Mathematical Science, Anhui University, Hefei 230601, China
2.
State Key Laboratory of Cognitive Neuroscience and Learning IDG/McGovern Institute for Brain & Research, School of Systems Science, Beijing Normal University, Beijing 100875, China

Corresponding author: Wang Wen-Xu, wenxuwang@bnu.edu.cn

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References

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Cited By

图 1 网络重构示意图　(a)通过离散的数据; (b)连续的数据; (c)推断网络结构

Figure 1. Illustration of network reconstruction: (a) By using the discrete data; (b) the continuous data; (c) reconstruct network.

DownLoad: Full-Size Img PowerPoint

图 2 基于压缩感知方法重构Karate网络中4号节点的邻居(重构方法见2.4节)

Figure 2. Reconstructing of node 4 in the Karate network based on compressive sensing framework (the reconstruction method is introduced in Subsec. 2.4).

DownLoad: Full-Size Img PowerPoint

图 3 驱动-响应实验示意图. 对稳态系统施加(稳态是一个稳定点(a), 或者一个周期轨道(b))一个持续驱动I, 系统达到另外一个稳态. 两个稳态的差异v包含了网络的拓扑结构

Figure 3. Driving-response experiments. System is shifted from one stable state (the stable state is a fixed point (a), or a periodical trajectory (b)) to another position by input a driving signal I. The difference of the trajectories contains information about the topology.

DownLoad: Full-Size Img PowerPoint

图 4 EM算法推断Karate网络33号节点的结构　(a)网络结构; (b)二进制数据; (c)EM算法推断出节点33的结构; (d)真实网络33号节点的结构

Figure 4. Reconstructing the neighbors of node 33 in Karate network: (a) The real structure of the Karate network; (b) the binary state data; (c) inferring the neighbors of node 33 based on EM algorithm; (d) the real neighbors of node 33.

DownLoad: Full-Size Img PowerPoint

[1]	Prigogine I, Hiebert E N 1982 Phys. Today 35 69
[2]	Haken H 2006 Information and Self-organization: A Macroscopic Approach to Complex Systems (Berlin: Springer)
[3]	Schrödinger E 1944 What is Life? The Physical Aspect of the Living Cell and Mind (Cambridge: Cambridge University Press)
[4]	Wilson E O 1992 The Diversity of Life (Boston: Belknap Press)
[5]	Wilson E O 2016 Half Earth: Our Planet’s Fight for Life (London: Liveright)
[6]	Lorenz E N 1963 J. Atmos. Sci. 20 130 Google Scholar
[7]	Conway J H 2000 On Numbers and Games (Boca Raton: AK Peters/CRC Press)
[8]	Ott E 2002 Chaos in Dynamical Systems (Cambridge: Cambridge University Press)
[9]	Barabási A L 2012 Nat. Phys. 8 14 Google Scholar
[10]	Downey A 2018 Think Complexity: Complexity Science and Computational Modeling (Sebastopol: O'Reilly Media)
[11]	Johnson N 2009 Simply Complexity: A Clear Guide to Complexity Theory (Oxford: Oneworld Publications)
[12]	Alberts B, Bray D, Hopkin K, Johnson A D, Lewis J, Raff M, Roberts K, Walter P 2013 Essential Cell Biology (New York: Garland Science)
[13]	Cartwright E 2018 Behavioral Economics (London: Routledge)
[14]	Newman M E J 2010 Networks: An Introduction (Oxford: Oxford University Press)
[15]	Newman M E J 2003 SIAM Rev. 45 167 Google Scholar
[16]	Boccaletti S, Latora V, Moreno Y, Chavez M, Hwang D U 2006 Phys. Rep. 424 175 Google Scholar
[17]	Pastor-Satorras R, Castellano C, van Mieghem P, Vespignani A 2015 Rev. Mod. Phys. 87 925 Google Scholar
[18]	Liu Y Y, Barabási A L 2016 Rev. Mod. Phys. 88 035006 Google Scholar
[19]	Stankovski T, Pereira T, McClintock P V E, Stefanovska A 2017 Rev. Mod. Phys. 89 045001 Google Scholar
[20]	Timme M, Casadiego J 2014 J. Phys. A: Math. Theor. 47 343001 Google Scholar
[21]	Wang W X, Lai Y C, Grebogi C 2016 Phys. Rep. 644 1 Google Scholar
[22]	陆君安, 吕金虎, 刘慧, 陈娟 2010 复杂系统与复杂性科学 7 63 Google Scholar Lu J A, Lu J H, Liu H, Chen J 2010 Complex Systems and Complexity Science 7 63 Google Scholar
[23]	王文旭 2013 电子科技大学学报 42 3 Wang W X 2013 Journal of Electronic Science and Technology 42 3
[24]	Qin S J 2012 Annu. Rev. Control 36 2
[25]	张朝阳, 陈阳, 弭元元, 胡岗 2020 中国科学: 物理学力学天文学 1 3 Zhang Z Y, Chen Y, Mi Y Y, Hu G 2020 Sci. Sin.-Phys. Mech. Astron. 1 3
[26]	Candes E J, Tao T 2006 IEEE Trans. Inf. Theory 52 5406 Google Scholar
[27]	Romberg J 2008 IEEE Signal Process. Mag. 25 14
[28]	Candes E J, Wakin M B 2008 IEEE Signal Process. Mag. 25 21 Google Scholar
[29]	Candes E J, Romberg J, Tao T 2006 IEEE Trans. Inf. Theory 52 489 Google Scholar
[30]	Baraniuk R G 2007 IEEE Signal Process. Mag. 24 118
[31]	Wang W X, Yang R, Lai Y C, Kovanis V, Harrison M A F 2011 EPL 94 48006 Google Scholar
[32]	Su R Q, Ni X, Wang W X, Lai Y C 2012 Phys. Rev. E 85 056220 Google Scholar
[33]	Szabó G, Fáth G 2007 Phys. Rep. 446 97 Google Scholar
[34]	Nowak M A, May R M 1992 Nature 359 826 Google Scholar
[35]	Wang W X, Lai Y C, Grebogi C, Ye J P 2011 Phys. Rev. X 1 290
[36]	Ma L, Han X, Shen Z S, Wang W X, Di Z R 2015 PLoS ONE 10 0142837
[37]	Han X, Shen Z S, Wang W X, Lai Y C, Grebogi C 2016 Sci. Rep. 6 30241 Google Scholar
[38]	Dorogovtsev S N, Goltsev A V, Mendes J F F 2002 Phy. Rev. E 66 16104 Google Scholar
[39]	Pastor-Satorras R, Vespignani A 2001 Phys. Rev. E 63 066117 Google Scholar
[40]	Nowak M A, May R M 1993 Int. J. Bifurcation Chaos 3 35 Google Scholar
[41]	Wang Y, Xiao G, Liu J 2012 New J. Phys. 14 13015 Google Scholar
[42]	Shen Z S, Wang W X, Fan Y, Di Z R, Lai Y C 2014 Nat. Commun. 5 4323 Google Scholar
[43]	Li J, Shen Z S, Wang W X, Grebogi C, Lai Y C 2017 Phys. Rev. E 95 032303
[44]	Wang W X, Yang R, Lai Y C, Kovanis V, Grebogi C 2011 Phys. Rev. Lett. 106 154101 Google Scholar
[45]	Su R Q, Wang W X, Wang X, Lai Y C 2016 R. Soc. Open Sci. 3 150577 Google Scholar
[46]	Su R Q, Wang W X, Lai Y C 2012 Phys. Rev. E 85 065201 Google Scholar
[47]	Tang S Q, Shen Z S, Wang W X, Di Z R 2015 Eur. Phys. J. B 88 211 Google Scholar
[48]	Chen Y Z, Lai Y C 2018 Phys. Rev. E 97 032317
[49]	Li G J, Li N, Liu S H, Wu X Q 2019 Chaos 29 53117 Google Scholar
[50]	Mei G F, Wu X Q, Wang Y F, Hu M, Lu J A, Chen G R 2018 IEEE Trans. Cybern. 48 754 Google Scholar
[51]	Wang X, Lu J H, Wu X Q 2018 IEEE Trans. Syst. Man Cybern. Part A Syst. HumansGoogle Scholar
[52]	Liu J, Mei G F, Wu X Q, Lu J H 2018 IEEE Trans. Circuits Syst. I 65 2970 Google Scholar
[53]	Shandilya S G, Timme M 2011 New J. Phys. 13 13004 Google Scholar
[54]	Han X, Shen Z S, Wang W X, Di Z R 2015 Phys. Rev. Lett. 114 028701 Google Scholar
[55]	Yu D, Righero M, Kocarev L 2006 Phys. Rev. Lett. 97 188701 Google Scholar
[56]	Zhou J, Lu J A 2007 Physica A 386 481 Google Scholar
[57]	Liu H, Lu J A, Lü J H, Hill D J 2009 Automatica 45 1799 Google Scholar
[58]	Wu X Q, Zhao X Y, Lu J H, Tang L K, Lu J A 2016 IEEE Trans. Control Netw. Syst. 3 379 Google Scholar
[59]	Zhao X Y, Zhou J, Zhu S B, Ma C, Lu J A 2019 IEEE Trans. Circuits Syst. II 67 290 Google Scholar
[60]	Chen L, Lu J A, Tse C K 2009 IEEE Trans. Circuits Syst. II 56 310 Google Scholar
[61]	Zhou J, Yu W W, Li X M, Small M, Lu J A 2009 IEEE Trans. Neural Networks 20 1679 Google Scholar
[62]	Zhu S B, Zhou J, Chen G R, Lu J A 2019 IEEE Trans. Cybern.Google Scholar
[63]	Zhu S B, Zhou J, Lu J A 2018 Chaos 28 43108 Google Scholar
[64]	杨浦, 郑志刚 2012 物理学报 61 120508 Google Scholar Yang P, Zheng Z G 2012 Acta Phys. Sin. 61 120508 Google Scholar
[65]	Gardner T S, Di Bernardo D, Lorenz D, Collins J J 2003 Science 301 102 Google Scholar
[66]	Tegner J, Yeung M K S, Hasty J, Collins J J 2003 Proc. Natl. Acad. Sci. 100 5944 Google Scholar
[67]	Yeung M K S, Tegnér J, Collins J J 2002 Proc. Natl. Acad. Sci. 99 6163 Google Scholar
[68]	Timme M 2007 Phys. Rev. Lett. 98 224101 Google Scholar
[69]	Yu D C 2010 Automatica 46 2035 Google Scholar
[70]	Yu D C, Parlitz U 2010 Phys. Rev. E 82 026108 Google Scholar
[71]	Ren J, Wang W X, Li B W, Lai Y C 2010 Phys. Rev. Lett. 104 058701 Google Scholar
[72]	Wang W X, Ren J, Lai Y C, Li B W 2012 Chaos 22 33131 Google Scholar
[73]	Zhang Z Y, Chen Y, Mi Y Y, Hu G 2019 Phys. Rev. E 99 042311 Google Scholar
[74]	Zhang Z Y, Zheng Z G, Niu H J, Mi Y Y, Wu S, Hu G 2015 Phys. Rev. E 91 012814 Google Scholar
[75]	马闯 2019 博士学位论文 (合肥: 安徽大学) Ma C 2019 Ph. D. Dissertation (Hefei: Anhui University) (in Chinese)
[76]	Ma C, Chen H S, Li X, Lai Y C, Zhang H F 2020 SIAM J. Appl. Dyn. 19 124 Google Scholar
[77]	Xiang B B, Ma C, Chen H S, Zhang H F 2018 Chaos 28 123117 Google Scholar
[78]	Liu Q M, Ma C, Xiang B B, Chen H S, Zhang H F 2019 IEEE Trans. Syst. Man Cybern. Syst.Google Scholar
[79]	Ma C, Chen H S, Lai Y C, Zhang H F 2018 Phys. Rev. E 97 22301
[80]	Zhang H F, Xu F, Bao Z K, Ma C 2019 IEEE Trans Circuits Syst. Regul Pap. 66 1608 Google Scholar
[81]	Ma C, Zhang H F, Lai Y C 2017 Phys. Rev. E 96 022320
[82]	Wu X Q, Wang W H, Zheng W X 2012 Phys. Rev. E 86 046106 Google Scholar
[83]	Wu X Q, Zhou C S, Chen G R, Lu J A 2011 Chaos 21 43129 Google Scholar
[84]	Li X, Li X 2017 Nat. Commun. 8 15729
[85]	Casadiego J, Nitzan M, Hallerberg S, Timme M 2017 Nat. Commun. 8 2192 Google Scholar

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