Synchronizability of multilayer star-ring networks with variable coupling strength

Shuang Liu; Bigang Xu; Qingyun Wang; Xia Tan; Shuang Liu; Bigang Xu; Qingyun Wang; Xia Tan

doi:10.3934/era.2023316

Electronic Research Archive

2023, Volume 31, Issue 10: 6236-6259. doi: 10.3934/era.2023316

Previous Article Next Article

Research article Special Issues

Synchronizability of multilayer star-ring networks with variable coupling strength

1.
Shanghai Engineering Research Center of Physical Vapor Deposition (PVD) Superhard Coating and Equipment, Shanghai Institute of Technology, Shanghai 201418, China
2.
Department of Dynamics and Control, Beihang University, Beijing 100191, China

Received: 26 June 2023 Revised: 20 August 2023 Accepted: 11 September 2023 Published: 20 September 2023

We investigate the synchronizability of multilayer star-ring networks. Two types of multilayer networks, including aggregated coupling and divergent coupling, are established based on the connections between the hub node and the leaf nodes in the subnetwork. The eigenvalue spectrum of the two types of multilayer networks is strictly derived, and the correlation between topological parameters and synchronizability is analyzed by the master stability function framework. Moreover, the variable coupling strength has been investigated, revealing that it is significantly related to the synchronizability of the aggregated coupling while having no influence on the divergent coupling. Furthermore, the validity of the synchronizability analysis is obtained by implementing adaptive control on the multilayer star-ring networks previously mentioned. Calculations and comparisons show that the differences caused by the sizes of multilayer networks and interlayer coupling strength are not negligible. Finally, numerical examples are also provided to validate the effectiveness of the theoretical analysis.
- multilayer networks,
- synchronizability,
- eigenvalue spectrum,
- coupling strength,
- time-varying topology
Citation: Shuang Liu, Bigang Xu, Qingyun Wang, Xia Tan. Synchronizability of multilayer star-ring networks with variable coupling strength[J]. Electronic Research Archive, 2023, 31(10): 6236-6259. doi: 10.3934/era.2023316

Related Papers:

Abstract

We investigate the synchronizability of multilayer star-ring networks. Two types of multilayer networks, including aggregated coupling and divergent coupling, are established based on the connections between the hub node and the leaf nodes in the subnetwork. The eigenvalue spectrum of the two types of multilayer networks is strictly derived, and the correlation between topological parameters and synchronizability is analyzed by the master stability function framework. Moreover, the variable coupling strength has been investigated, revealing that it is significantly related to the synchronizability of the aggregated coupling while having no influence on the divergent coupling. Furthermore, the validity of the synchronizability analysis is obtained by implementing adaptive control on the multilayer star-ring networks previously mentioned. Calculations and comparisons show that the differences caused by the sizes of multilayer networks and interlayer coupling strength are not negligible. Finally, numerical examples are also provided to validate the effectiveness of the theoretical analysis.

References

[1]	R. Albert, A. L. Barabási, Statistical mechanics of complex networks, Rev. Mod. Phys., 74 (2002), 47–97. https://doi.org/10.1103/RevModPhys.74.47 doi: 10.1103/RevModPhys.74.47
[2]	A. L. Barabasi, Z. N. Oltvai, Network biology: understanding the cell's functional organization, Nat. Rev. Genet., 5 (2004), 101–113. https://doi.org/10.1038/nrg1272 doi: 10.1038/nrg1272
[3]	M. E. J. Newman, Communities, modules and large-scale structure in networks, Nat. Phys., 8 (2012), 25–31. https://doi.org/10.1038/nphys2162 doi: 10.1038/nphys2162
[4]	J. Lin, Y. Ban, Complex network topology of transportation systems, Transport Rev., 33 (2013), 658–685. https://doi.org/10.1080/01441647.2013.848955 doi: 10.1080/01441647.2013.848955
[5]	R. E. Mirollo, S. H. Strogatz, Synchronization of pulse-coupled biological oscillators, SIAM J. Appl. Math., 50 (1990), 1645–1662. https://doi.org/10.1137/0150098 doi: 10.1137/0150098
[6]	X. Zhang, S. Boccaletti, S. Guan, Z. Liu, Explosive synchronization in adaptive and multilayer networks, Phys. Rev. Lett., 114 (2015), 038701. https://doi.org/10.1103/PhysRevLett.114.038701 doi: 10.1103/PhysRevLett.114.038701
[7]	P. Wang, G. Wen, X. Yu, W. Yu, T. Huang, Synchronization of multi-layer networks: from node-to-node synchronization to complete synchronization, IEEE Trans. Circuits Syst. I Regul. Pap., 66 (2018), 1141–1152. https://doi.org/10.1109/TCSI.2018.2877414 doi: 10.1109/TCSI.2018.2877414
[8]	H. Liu, Y. Li, Z. Li, J. Lü, J. Lu, Topology identification of multilink complex dynamical networks via adaptive observers incorporating chaotic exosignals, IEEE Trans. Cybern., 52 (2022), 6255–6268. https://doi.org/10.1109/TCYB.2020.3042223 doi: 10.1109/TCYB.2020.3042223
[9]	G. Mei, X. Wu, Y. Wang, M. Hu, J. Lu, G. Chen, Compressive-sensing-based structure identification for multilayer networks, IEEE Trans. Cybern., 48 (2017), 754–764. https://doi.org/10.1109/TCYB.2017.2655511 doi: 10.1109/TCYB.2017.2655511
[10]	X. Wang, A. Tejedor, Y. Wang, Y. Moreno, Unique superdiffusion induced by directionality in multiplex networks, New J. Phys., 23 (2021), 013016. https://doi.org/10.1088/1367-2630/abdb71 doi: 10.1088/1367-2630/abdb71
[11]	M. Turalska, K. Burghardt, M. Rohden, A. Swami, R. M. D'Souza, Cascading failures in scale-free interdependent networks, Phys. Rev. E: Stat. Nonlinear Soft Matter Phys., 99 (2019), 032308. https://doi.org/10.1103/PhysRevE.99.032308 doi: 10.1103/PhysRevE.99.032308
[12]	J. Chang, X. Yin, C. Ma, D. Zhao, Y. Sun, Estimation of the time cost with pinning control for stochastic complex networks, Electron. Res. Arch., 30 (2022), 3509–3526. https://doi.org/10.3934/era.2022179 doi: 10.3934/era.2022179
[13]	S. S. Sajjadi, D. Baleanu, A. Jajarmi, H. M. Pirouz, A new adaptive synchronization and hyperchaos control of a biological snap oscillator, Chaos, Solitons Fractals, 138 (2020), 109919. https://doi.org/10.1016/j.chaos.2020.109919 doi: 10.1016/j.chaos.2020.109919
[14]	S. Liu, R. Zhang, Q. Wang, X. He, Sliding mode synchronization between uncertain Watts-Strogatz small-world spatiotemporal networks, Appl. Math. Mech., 41 (2020), 1833–1846. https://doi.org/10.1007/s10483-020-2686-6 doi: 10.1007/s10483-020-2686-6
[15]	K. Hengster-Movric, K. You, F. L. Lewis, L. Xie, Synchronization of discrete-time multi-agent systems on graphs using Riccati design, Automatica, 49 (2013), 414–423. https://doi.org/10.1016/j.automatica.2012.11.038 doi: 10.1016/j.automatica.2012.11.038
[16]	L. M. Pecora, T. L. Carrollton, Synchronization in chaotic systems, Phys. Rev. Lett., 64 (1990), 821–827. https://doi.org/10.1103/PhysRevLett.64.821 doi: 10.1103/PhysRevLett.64.821
[17]	Z. Wu, X. Fu, Complex projective synchronization in drive-response networks coupled with complex-variable chaotic systems, Nonlinear Dyn., 72 (2013), 9–15. https://doi.org/10.1007/s11071-012-0685-7 doi: 10.1007/s11071-012-0685-7
[18]	H. Hong, M. Y. Choi, B. J. Kim, Synchronization on small-world networks, Phys. Rev. E: Stat. Nonlinear Soft Matter Phys., 65 (2002), 026139. https://doi.org/10.1103/PhysRevE.65.026139 doi: 10.1103/PhysRevE.65.026139
[19]	K. Li, S. Guan, X. Gong, C. H. Lai, Synchronization stability of general complex dynamical networks with time-varying delays, Phys. Lett. A, 372 (2008), 7133–7139. https://doi.org/10.1016/j.physleta.2008.10.054 doi: 10.1016/j.physleta.2008.10.054
[20]	X. Zhao, J. Zhou, J. Lu, Pinning synchronization of multiplex delayed networks with stochastic perturbations, IEEE Trans. Cybern., 49 (2018), 4262–4270. https://doi.org/10.1109/TCYB.2018.2861822 doi: 10.1109/TCYB.2018.2861822
[21]	A. Fan, J. Li, J. Li, Adaptive event-triggered prescribed performance learning synchronization for complex dynamical networks with unknown time-varying coupling strength, Nonlinear Dyn., 100 (2020), 2575–2593. https://doi.org/10.1007/s11071-020-05648-w doi: 10.1007/s11071-020-05648-w
[22]	S. Gomez, A. Diaz-Guilera, J. Gomez-Gardenes, C. J. Pérez-Vicente, Y. Moreno, A. Arenas, Diffusion dynamics on multiplex networks, Phys. Rev. Lett., 110 (2013), 028701. https://doi.org/10.1103/PhysRevLett.110.028701 doi: 10.1103/PhysRevLett.110.028701
[23]	J. A. Almendral, A. Díaz-Guilera, Dynamical and spectral properties of complex networks, New J. Phys., 9 (2007), 187. https://doi.org/10.1088/1367-2630/9/6/187 doi: 10.1088/1367-2630/9/6/187
[24]	C. Granell, S. Gómez, A. Arenas, Dynamical interplay between awareness and epidemic spreading in multiplex networks, Phys. Rev. Lett., 111 (2013), 128701. https://doi.org/10.1103/PhysRevLett.111.128701 doi: 10.1103/PhysRevLett.111.128701
[25]	J. Aguirre, R. Sevilla-Escoboza, R. Gutierrez, D. Papo, M. Buldú, Synchronization of interconnected networks: the role of connector nodes, Phys. Rev. Lett., 112 (2014), 248701. https://doi.org/10.1103/PhysRevLett.112.248701 doi: 10.1103/PhysRevLett.112.248701
[26]	M. Xu, J. Lu, J. Zhou, Synchronizability and eigenvalues of two-layer star networks (in Chinese), Acta Phys. Sin., 65 (2016), 028902. https://doi.org/10.7498/aps.65.028902 doi: 10.7498/aps.65.028902
[27]	J. Li, Y. Luan, X. Wu, J. Lu, Synchronizability of double-layer dumbbell networks, Chaos, 31 (2021), 073101. https://doi.org/10.1063/5.0049281 doi: 10.1063/5.0049281
[28]	Y. Deng, Z. Jia, F. Yang, Synchronizability of multilayer star and star-ring networks, Discrete Dyn. Nat. Soc., 2020 (2020), 9143917. https://doi.org/10.1155/2020/9143917 doi: 10.1155/2020/9143917
[29]	P. Peng, J. Wang, K. Huang, Reliable fiber sensor system with star-ring-bus architecture, Sensors, 10 (2010), 4194–4205. https://doi.org/10.3390/s100504194 doi: 10.3390/s100504194
[30]	C. Christodoulou, G. Ellinas, Resilient architecture for optical access networks, Photonic Network Commun., 41 (2021), 1–16. https://doi.org/10.1007/s11107-020-00910-y doi: 10.1007/s11107-020-00910-y
[31]	S. Liu, L. Chen, Second-order terminal sliding mode control for networks synchronization, Nonlinear Dyn., 79 (2015), 205–213. https://doi.org/10.1007/s11071-014-1657-x doi: 10.1007/s11071-014-1657-x
[32]	R. Li, H. Wu, J. Cao, Exponential synchronization for variable-order fractional discontinuous complex dynamical networks with short memory via impulsive control, Neural Networks, 148 (2022), 13–22. https://doi.org/10.1016/j.neunet.2021.12.021 doi: 10.1016/j.neunet.2021.12.021
[33]	Y. Tang, F. Qian, H. Gao, J. Kurths, Synchronization in complex networks and its application–a survey of recent advances and challenges, Annu. Rev. Control, 38 (2014), 184–198. https://doi.org/10.1016/j.arcontrol.2014.09.003 doi: 10.1016/j.arcontrol.2014.09.003
[34]	Y. Shi, Y. Ma, Finite/fixed-time synchronization for complex networks via quantized adaptive control, Electron. Res. Arch., 29 (2021), 2047–2061. https://doi.org/10.3934/era.2020104 doi: 10.3934/era.2020104
[35]	Z. Qin, J. Wang, Y. Huang, S. Ren, Analysis and adaptive control for robust synchronization and H_∞ synchronization of complex dynamical networks with multiple time-delays, Neurocomputing, 289 (2018), 241–251. https://doi.org/10.1016/j.neucom.2018.02.031 doi: 10.1016/j.neucom.2018.02.031
[36]	A. Zentani, N. Zulkifli, A. Ramli, Network resiliency and fiber usage of Tree, Star, ring and wheel based wavelength division multiplexed passive optical network Topologies: a comparative review, Opt. Fiber Technol., 73 (2022), 103038. https://doi.org/10.1016/j.yofte.2022.103038 doi: 10.1016/j.yofte.2022.103038
[37]	M. Xu, K. An, L. H. Vu, Z. Ye, J. Feng, E. Chen, Optimizing multi-agent based urban traffic signal control system, J. Intell. Transp. Syst., 23 (2019), 357–369. https://doi.org/10.1080/15472450.2018.1501273 doi: 10.1080/15472450.2018.1501273
[38]	L. Xing, Cascading failures in internet of things: review and perspectives on reliability and resilience, IEEE Internet Things J., 8 (2020), 44–64. https://doi.org/10.1109/JIOT.2020.3018687 doi: 10.1109/JIOT.2020.3018687
[39]	J. Wei, X. Wu, J. Lu, X. Wei, Synchronizability of duplex regular networks, EuroPhys. Lett., 120 (2018), 20005. https://doi.org/10.1209/0295-5075/120/20005 doi: 10.1209/0295-5075/120/20005
[40]	L. Tang, X. Wu, J. Lü, J. Lu, R. M. D'Souza, Master stability functions for complete, intralayer, and interlayer synchronization in multiplex networks of coupled Rössler oscillators, Phys. Rev. E: Stat. Nonlinear Soft Matter Phys., 99 (2019), 012304. https://doi.org/10.1103/PhysRevE.99.012304 doi: 10.1103/PhysRevE.99.012304
[41]	L. M. Pecora, T. L. Carroll, Master stability functions for synchronized coupled systems, Phys. Rev. Lett., 80 (1998), 2109. https://doi.org/10.1103/PhysRevLett.80.2109 doi: 10.1103/PhysRevLett.80.2109
[42]	J. Sun, X. Li, J. Zhang, Y. Shen, Y. Li, Synchronizability and eigenvalues of multilayer star networks through unidirectionally coupling (in Chinese), Acta Phys. Sin., 66 (2017), 188901. https://doi.org/10.7498/aps.66.188901 doi: 10.7498/aps.66.188901
[43]	X. Jin, Z. Wang, H. Yang, Q. Song, M. Xiao, Synchronization of multiplex networks with stochastic perturbations via pinning adaptive control, J. Franklin Inst., 358 (2021), 3994–4012. https://doi.org/10.1016/j.jfranklin.2021.03.004 doi: 10.1016/j.jfranklin.2021.03.004
[44]	X. Mao, A note on the LaSalle-type theorems for stochastic differential delay equations, J. Math. Anal. Appl., 268 (2002), 125–142. https://doi.org/10.1006/jmaa.2001.7803 doi: 10.1006/jmaa.2001.7803
[45]	F. Yang, Z. Jia, Y. Deng, Eigenvalue spectrum and synchronizability of two types of double-layer star-ring networks with hybrid directional coupling, Discrete Dyn. Nat. Soc., 2021 (2021), 1–20. https://doi.org/10.1155/2021/6623648 doi: 10.1155/2021/6623648
[46]	J. L. Hindmarsh, R. M. Rose, A model of the nerve impulse using two first-order differential equations, Nature, 296 (1982), 162–164. https://doi.org/10.1038/296162a0 doi: 10.1038/296162a0
[47]	L. Xu, G. Qi, J. Ma, Modeling of memristor-based Hindmarsh-Rose neuron and its dynamical analyses using energy method, Appl. Math. Modell., 101 (2022), 503–516. https://doi.org/10.1016/j.apm.2021.09.003 doi: 10.1016/j.apm.2021.09.003
[48]	L. Shi, C. Zhang, S. Zhong, Synchronization of singular complex networks with time-varying delay via pinning control and linear feedback control, Chaos, Solitons Fractals, 145 (2021), 110805. https://doi.org/10.1016/j.chaos.2021.110805. doi: 10.1016/j.chaos.2021.110805
[49]	Y. Deng, Z. Jia, G. Deng, Q. Zhang, Eigenvalue spectrum and synchronizability of multiplex chain networks, Physica A, 537 (2020), 122631. https://doi.org/10.1016/j.physa.2019.122631 doi: 10.1016/j.physa.2019.122631
[50]	Y. Li, X. Wu, J. Lu, J. Lü, Synchronizability of duplex networks, IEEE Trans. Circuits Syst. Ⅱ Express Briefs, 63 (2015), 206–210. https://doi.org/10.1109/TCSⅡ.2015.2468924 doi: 10.1109/TCSⅡ.2015.2468924

Reader Comments

Your name:*

Email:*
© 2023 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)