Attractive target wave patterns in complex networks consisting of excitable nodes

doi:10.1088/1674-1056/23/7/078906

Abstract This review describes the investigations of oscillatory complex networks consisting of excitable nodes, focusing on the target wave patterns or say the target wave attractors. A method of dominant phase advanced driving (DPAD) is introduced to reveal the dynamic structures in the networks supporting oscillations, such as the oscillation sources and the main excitation propagation paths from the sources to the whole networks. The target center nodes and their drivers are regarded as the key nodes which can completely determine the corresponding target wave patterns. Therefore, the center (say node A) and its driver (say node B) of a target wave can be used as a label, (A,B), of the given target pattern. The label can give a clue to conveniently retrieve, suppress, and control the target waves. Statistical investigations, both theoretically from the label analysis and numerically from direct simulations of network dynamics, show that there exist huge numbers of target wave attractors in excitable complex networks if the system size is large, and all these attractors can be labeled and easily controlled based on the information given by the labels. The possible applications of the physical ideas and the mathematical methods about multiplicity and labelability of attractors to memory problems of neural networks are briefly discussed.

Keywords: dominant phase advanced driving method complex networks labelable attractors target wave patterns

Received: 17 June 2014
Accepted manuscript online:

PACS:	89.75.Fb	(Structures and organization in complex systems)
	89.75.Kd	(Patterns)
	05.65.+b	(Self-organized systems)

Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 11174034, 11135001, 11205041, and 11305112) and the Natural Science Foundation of Jiangsu Province, China (Grant No. BK20130282).

Corresponding Authors: Hu Gang
E-mail: ganghu@bnu.edu.cn

Cite this article:

Zhang Li-Sheng (张立升), Liao Xu-Hong (廖旭红), Mi Yuan-Yuan (弭元元), Qian Yu (钱郁), Hu Gang (胡岗) Attractive target wave patterns in complex networks consisting of excitable nodes 2014 Chin. Phys. B 23 078906

[1]	Cross M C and Hohenberg P C 1993 Rev. Mod. Phys. 65 851;
[2]	Meron E 1992 Phys. Rep. 218 1;
[3]	Greenberg J M and Hastings S P 1978 SIAM J. Appl. Math. 34 515;
[4]	Winfree A T 1987 When Time Breaks Down (Princeton: Princeton University Press);
[5]	Tinsley M, Cui J, Chirila F V, Taylor A, Zhong S and Showalter K 2005 Phys. Rev. Lett. 95 038306;
[6]	Müller-Linow M, Hilgetag C C and HüttMT 2008 PLos Comput. Biol. 4e1000190;
[7]	Watts D J and Strogatz S H 1998 Nature 393 440;
[8]	Barabási A L and Albert R 1999 Science 286 509;
[9]	Dorogovtsev S N and Goltsev A V 2008 Rev. Mod. Phys. 80 1275;
[10]	Albert R and Barabási A L 2002 Rev. Mod. Phys. 74 47;
[11]	Kuperman M and Abramson G 2001 Phys. Rev. Lett. 86 2909;
[12]	Ji P, Peron T K D M, Menck P J, Rodrigues F A and Kurths J 2013 Phys. Rev. Lett. 110 218701;
[13]	Liao X, Xia Q, Qian Y, Zhang L, Hu G and Mi Y 2011 Phys. Rev. E 83 056204;
[14]	Mi Y, Zhang L, Huang X, Qian Y, Hu G and Liao X 2011 Europhys. Lett. 95 58001;
[15]	Zhang Z, Ye W, Qian Y, Zheng Z, Huang X and Hu G 2012 PLoS One 7e39355;
[16]	Mi Y, Liao X, Huang X, Zhang L, Gu W, Hu G and Wu S 2013 Proc. Natl. Acad. Sci. USA 110 E4931;
[17]	Belik V, Geisel T and Brockmann D 2011 Phys. Rev. X 1 011001;
[18]	Liao X H, Qian Y, Mi Y Y, Huang X D, Xia Q Z and Hu G 2011 Front. Phys. 6 124;
[19]	Liao X H, Ye W M, Huang X D, Xia Q Z, Huang X Q, Li P F, Qian Y, Huang X D and Hu G 2009 arXiv:0906.2356v3;
[20]	Fu C, Zhang H, Zhan M and Wang X 2012 Phys. Rev. E 85 066208;
[21]	Zhang L, GuW, Liao X,Wang Y, Hu G and Mi Y 2012 Europhys. Lett. 99 18005;
[22]	Qian Y, Liao X, Huang X, Mi Y, Zhang L and Hu G 2010 Phys. Rev. E 82 026107;
[23]	Bär M and Eiswirth M 1993 Phys. Rev. E 48 R1635;
[24]	D’Souza R M 2009 Nat. Phys. 5 627;
[25]	Erdős P and Réyi A 1959 Publ. Math. (Debrecen) 6 290;
[26]	Bollobás B 1998 Modern Graph Theory (New York: Springer-Verlag);
[27]	Gerstner W and Kistler W M 2002 Spiking Neuron Models (Cambridge: Cambridge University Press);
[28]	Moody S L, Wise S P, Pellegrino G di and Zipser D 1998 J Neurosci 18 399;
[29]	Neiman T and Loewenstein Y 2013 J Neurosci 33 1521;
[30]	Rabinovich M, Huerta R and Laurent G 2008 Science 321 48;
[31]	Wills T J, Lever C, Cacucci F and Burgess N 2005 Science 308 873;
[32]	Mazor O and Laurent G 2005 Neuron 48 661;
[33]	Poucet B and Save E 2005 Science 308 799

[1]	Analysis of cut vertex in the control of complex networks Jie Zhou(周洁), Cheng Yuan(袁诚), Zu-Yu Qian(钱祖燏), Bing-Hong Wang(汪秉宏), and Sen Nie(聂森). Chin. Phys. B, 2023, 32(2): 028902.
[2]	Vertex centrality of complex networks based on joint nonnegative matrix factorization and graph embedding Pengli Lu(卢鹏丽) and Wei Chen(陈玮). Chin. Phys. B, 2023, 32(1): 018903.
[3]	Characteristics of vapor based on complex networks in China Ai-Xia Feng(冯爱霞), Qi-Guang Wang(王启光), Shi-Xuan Zhang(张世轩), Takeshi Enomoto(榎本刚), Zhi-Qiang Gong(龚志强), Ying-Ying Hu(胡莹莹), and Guo-Lin Feng(封国林). Chin. Phys. B, 2022, 31(4): 049201.
[4]	Robust H_∞ state estimation for a class of complex networks with dynamic event-triggered scheme against hybrid attacks Yahan Deng(邓雅瀚), Zhongkai Mo(莫中凯), and Hongqian Lu(陆宏谦). Chin. Phys. B, 2022, 31(2): 020503.
[5]	Finite-time synchronization of uncertain fractional-order multi-weighted complex networks with external disturbances via adaptive quantized control Hongwei Zhang(张红伟), Ran Cheng(程然), and Dawei Ding(丁大为). Chin. Phys. B, 2022, 31(10): 100504.
[6]	LCH: A local clustering H-index centrality measure for identifying and ranking influential nodes in complex networks Gui-Qiong Xu(徐桂琼), Lei Meng(孟蕾), Deng-Qin Tu(涂登琴), and Ping-Le Yang(杨平乐). Chin. Phys. B, 2021, 30(8): 088901.
[7]	Complex network perspective on modelling chaotic systems via machine learning Tong-Feng Weng(翁同峰), Xin-Xin Cao(曹欣欣), and Hui-Jie Yang(杨会杰). Chin. Phys. B, 2021, 30(6): 060506.
[8]	Exploring individuals' effective preventive measures against epidemics through reinforcement learning Ya-Peng Cui(崔亚鹏), Shun-Jiang Ni (倪顺江), and Shi-Fei Shen(申世飞). Chin. Phys. B, 2021, 30(4): 048901.
[9]	Influential nodes identification in complex networks based on global and local information Yuan-Zhi Yang(杨远志), Min Hu(胡敏), Tai-Yu Huang(黄泰愚). Chin. Phys. B, 2020, 29(8): 088903.
[10]	Identifying influential spreaders in complex networks based on entropy weight method and gravity law Xiao-Li Yan(闫小丽), Ya-Peng Cui(崔亚鹏), Shun-Jiang Ni(倪顺江). Chin. Phys. B, 2020, 29(4): 048902.
[11]	Modeling and analysis of the ocean dynamic with Gaussian complex network Xin Sun(孙鑫), Yongbo Yu(于勇波), Yuting Yang(杨玉婷), Junyu Dong(董军宇)†, Christian B\"ohm, and Xueen Chen(陈学恩). Chin. Phys. B, 2020, 29(10): 108901.
[12]	Pyramid scheme model for consumption rebate frauds Yong Shi(石勇), Bo Li(李博), Wen Long(龙文). Chin. Phys. B, 2019, 28(7): 078901.
[13]	Theoretical analyses of stock correlations affected by subprime crisis and total assets: Network properties and corresponding physical mechanisms Shi-Zhao Zhu(朱世钊), Yu-Qing Wang(王玉青), Bing-Hong Wang(汪秉宏). Chin. Phys. B, 2019, 28(10): 108901.
[14]	Coordinated chaos control of urban expressway based on synchronization of complex networks Ming-bao Pang(庞明宝), Yu-man Huang(黄玉满). Chin. Phys. B, 2018, 27(11): 118902.
[15]	Detecting overlapping communities based on vital nodes in complex networks Xingyuan Wang(王兴元), Yu Wang(王宇), Xiaomeng Qin(秦小蒙), Rui Li(李睿), Justine Eustace. Chin. Phys. B, 2018, 27(10): 100504.

No Suggested Reading articles found!

Viewed

Full text

Abstract

Cited

Metrics
Related Articles

Attractive target wave patterns in complex networks consisting of excitable nodes

Cite this article:

Online attention