基于频率权重耦合模型的多层复杂网络爆发式同步

doi:10.12066/j.issn.1007-2861.2131

上海大学学报(自然科学版) ›› 2021, Vol. 27 ›› Issue (3): 492-502.doi: 10.12066/j.issn.1007-2861.2131

基于频率权重耦合模型的多层复杂网络爆发式同步

金彦亮(), 姚林, 王雪, 罗雪涛

上海大学通信与信息工程学院, 上海 200444

收稿日期:2019-03-18 出版日期:2021-06-30 发布日期:2021-06-27
通讯作者: 金彦亮 E-mail:jinyanliang@staff.shu.edu.cn
作者简介:金彦亮(1973—), 副教授, 博士, 研究方向为无线传感器网络、移动通信等. E-mail: jinyanliang@staff.shu.edu.cn
基金资助:
上海市科委资助项目(19511102803)

Explosive synchronisation of multi-layer networks based on frequency-weighted coupled model

JIN Yanliang(), YAO Lin, WANG Xue, LUO Xuetao

School of Communication and Information Engineering, Shanghai University, Shanghai 200444, China

Received:2019-03-18 Online:2021-06-30 Published:2021-06-27
Contact: JIN Yanliang E-mail:jinyanliang@staff.shu.edu.cn

摘要/Abstract

摘要：

同步现象是复杂网络和系统中普遍存在的一种动力学行为. 针对多层复杂网络上产生爆发式同步的临界耦合强度问题, 提出一种多层频率权重耦合的 Kuramoto 模型, 通过平均场思想和自洽理论分析求出多层复杂网络上产生爆发式同步时的临界耦合强度值, 并进行了仿真验证. 理论分析和仿真结果表明, 该临界值与层间相互作用强度和网络平均度相关, 层与层之间的相互作用增强会阻碍爆发式同步的产生, 而网络平均度增大会促进爆发式同步的产生. 这一结果对复杂网络和复杂系统的研究具有重要意义.

关键词: 多层网络, 临界耦合强度, 爆发式同步

Abstract:

Synchronisation is a prevalent and universal dynamic behaviour of complex systems. Based on the critical coupling strength of explosive synchronisation in multi-layer complex networks, a frequency-weighted Kuramoto model was developed in this study. We obtained the critical coupling strength for explosive synchronisation through field tests, self-consistent analysis, and numerical simulation. The theoretical analysis and simulation results show that the critical value is related to the strength of the interlayer interaction and the average degree of the network. Increasing the interaction between layers prevents explosive synchronisation, whereas increasing the average degree of the network facilitates explosive synchronisation. The results are useful for studies on complex networks and systems.

Key words: multi-layer networks, critical coupling strength, explosive synchronisation

中图分类号:

TN711.4

金彦亮, 姚林, 王雪, 罗雪涛. 基于频率权重耦合模型的多层复杂网络爆发式同步[J]. 上海大学学报(自然科学版), 2021, 27(3): 492-502.

JIN Yanliang, YAO Lin, WANG Xue, LUO Xuetao. Explosive synchronisation of multi-layer networks based on frequency-weighted coupled model[J]. Journal of Shanghai University（Natural Science Edition）, 2021, 27(3): 492-502.

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参考文献 20

[1]	Strogatz S H. Exploring complex networks[J]. Nature, 2001,410(6825):268-276. pmid: 11258382
[2]	Newman M. Networks: an introduction[J]. Astronomische Nachrichten, 2010,327(8):741-743. doi: 10.1002/(ISSN)1521-3994
[3]	Albert R, Barabasi A L. Statistical mechanics of complex networks [J]. Review of Modern Physics, 2001, 74(1): xii.
[4]	Dietert H. Stability and bifurcation for the Kuramoto model[J]. Journal De Mathématiques Pures Et Appliquées, 2016,105(4):451-489. doi: 10.1016/j.matpur.2015.11.001
[5]	Zhang F, Liao X, Zhang G. Some new results for the generalized Lorenz system[J]. Qualitative Theory of Dynamical Systems, 2016,16(3):1-11. doi: 10.1007/s12346-016-0188-x
[6]	Fitzhugh R. Computation of impulse initiation and saltatory conduction in a myelinated nerve fiber[J]. Biophysical Journal, 1962,2(1):11-21. doi: 10.1016/S0006-3495(62)86837-4
[7]	Nagumo J, Arimoto S, Yoshizawa S. An active pulse transmission line simulating nerve axon[J]. Proceedings of the IRE, 1962,50(10):2061-2070. doi: 10.1109/JRPROC.1962.288235
[8]	Gómez-Gardenes J, Gómez S, Arenas A, et al. Explosive synchronization transitions in scale-free networks[J]. Physical Review Letters, 2011,106(12):128701. doi: 10.1103/PhysRevLett.106.128701
[9]	Li P, Zhang K, Xu X, et al. Reexamination of explosive synchronization in scale-free networks: the effect of disassortativity[J]. Physical Review E: Statistical, Nonlinear & Soft Matter Physics, 2013,87(4-B):1-5.
[10]	Leyva I, Sendina-Nadal I, Almendral J A, et al. Explosive synchronization in weighted complex networks[J]. Physical Review E: Statistical, Nonlinear & Sofo Matter Physics, 2013,88(4):042808.
[11]	Zhang X, Hu X, Kurths J, et al. Explosive synchronization in a general complex network[J]. Physical Review E: Statistical, Nonlinear & Soft Matter Physics, 2013,88(1):010802.
[12]	Zhou W, Chen L, Bi H, et al. Explosive synchronization with asymmetric frequency distribution[J]. Physical Review E, 2015,92(1):012812. doi: 10.1103/PhysRevE.92.012812
[13]	Rosato V, Issacharoff L, Tiriticco F, et al. Modelling interdependent infrastructures using interacting dynamical models[J]. International Journal of Critical Infrastructures, 2016,4(1/2):63-79. doi: 10.1504/IJCIS.2008.016092
[14]	Schneider C M, Yazdani N, Araújo N A M, et al. Towards designing robust coupled networks[J]. Scientific Reports, 2013,3:1969-1977. doi: 10.1038/srep01969
[15]	Su G, Ruan Z, Guan S, et al. Explosive synchronization on co-evolving networks[J]. EPL (Europhysics Letters), 2013,103(4):48004. doi: 10.1209/0295-5075/103/48004
[16]	Zhang X, Boccaletti S, Guan S, et al. Explosive synchronization in adaptive and multilayer networks[J]. Physical Review Letters, 2015,114(3):038701. doi: 10.1103/PhysRevLett.114.038701
[17]	Jiang X, Li M, Zheng Z, et al. Effect of externality in multiplex networks on one-layer synchronization[J]. Journal of the Korean Physical Society, 2015,66(11):1777-1782. doi: 10.3938/jkps.66.1777
[18]	Kachhvah A D, Jalan S. Multiplexing induced explosive synchronization in Kuramoto oscillators with inertia[J]. EPL (Europhysics Letters), 2017,119(6):60005-60011. doi: 10.1209/0295-5075/119/60005
[19]	Restrepo J G, Hunt B R, Ott E. The onset of synchronization in large networks of coupled oscillators[J]. Physical Review E, 2005,71:036151. doi: 10.1103/PhysRevE.71.036151
[20]	Pikovsky A, Rosenblum M. Dynamics of globally coupled oscillators: progress and perspectives[J]. Chaos: An Interdisciplinary Journal of Nonlinear Science, 2015,25(9):097616. doi: 10.1063/1.4922971

基于频率权重耦合模型的多层复杂网络爆发式同步

Explosive synchronisation of multi-layer networks based on frequency-weighted coupled model

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