Skip to main content
SpringerLink
Log in

Synchronizability of time-varying structured duplex dynamical networks with different intra-layer rewiring mechanisms

  • Article
  • Published:
Science China Technological Sciences Aims and scope Submit manuscript

Abstract

Global synchronizability of duplex networks induced by three different intra-layer rewiring mechanisms is explored in this paper. The rewiring mechanisms are named as model-preserving rewiring (MPR), simply direct rewiring (SDR), and degree-preserving rewiring (DPR), respectively. It is found that high switching frequencies will certainly enhance global synchronizability for WS-WS duplex networks (i.e., each layer is independently formed by the algorithm proposed by Watts and Strogatz for generating small-world networks), ER-ER duplex networks (i.e., each layer is independently generated by the algorithm proposed by Erdös and Renyi) and BA-BA duplex networks (i.e., each layer is independently formed by the classical BA algorithm). Namely, the faster the intra-layer couplings are reconnected, the faster the duplex networks reach global synchronization. Furthermore, we find that by increasing the intra- or inter-coupling strengths, the WS-WS time-varying network’s global synchronizability is enhanced. Take the WS-WS time-varying network as an example, we find that SDR mechanism has greater impact on global synchronizability than MPR mechanism and DPR mechanism. The related dynamical networks can arrive at synchronization faster by SDR than by MPR or DPR. Thus, we only study the effects of SDR on ER-ER duplex networks and BA-BA duplex networks. In addition, we obtain the fact via numerical simulations that, switching intra-layer coupling topologies under SDR mechanism has the greatest impact on the BA-BA duplex network, followed by the ER-ER network, and has the weakest influence on the WS-WS duplex network in terms of improving the global synchronizability when all the intra-layer networks are sparse and have the same average degree. Finally, the global synchronizability of WS-WS and BA-BA time-varying networks is improved compared with static duplex networks, the reason being that the networks tend to be randomized under SDR according to analysis of the networks’ average clustering coefficients and degree distributions.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Wang X, Gu H B, Wang Q Y, et al. Identifying topologies and system parameters of uncertain time-varying delayed complex networks. Sci China Tech Sci, 2019, 62: 94–105

    Article  Google Scholar 

  2. Tang L K, Lu J A, Lü J H. A threshold effect of coupling delays on intra-layer synchronization in duplex networks. Sci China Tech Sci, 2018, 61: 1907–1914

    Article  Google Scholar 

  3. Wang Y F, Wu X Q, Feng H, et al. Topology inference of uncertain complex dynamical networks and its applications in hidden nodes detection. Sci China Tech Sci, 2016, 59: 1232–1243

    Article  Google Scholar 

  4. Aouiti C, Li X D, Miaadi F. Finite-time stabilization of uncertain delayed-hopfield neural networks with a time-varying leakage delay via non-chattering control. Sci China Tech Sci, 2019, 62: 1111–1122

    Article  Google Scholar 

  5. Cheng Z S, Xin Y M, Cao J D, et al. Selecting pinning nodes to control complex networked systems. Sci China Tech Sci, 2018, 61: 1537–1545

    Article  Google Scholar 

  6. Li N, Wu X, Feng J, et al. Fixed-time synchronization of complex dynamical networks: A novel and economical mechanism. IEEE Trans Cybern, 2020, doi: https://doi.org/10.1109/TCYB.2020.3026996

  7. Li X, Shen J, Rakkiyappan R. Persistent impulsive effects on stability of functional differential equations with finite or infinite delay. Appl Math Computation, 2018, 329: 14–22

    Article  MathSciNet  MATH  Google Scholar 

  8. Yang D, Li X, Qiu J. Output tracking control of delayed switched systems via state-dependent switching and dynamic output feedback. Nonlinear Anal-Hybrid Syst, 2019, 32: 294–305

    Article  MathSciNet  MATH  Google Scholar 

  9. Mei G, Wu X, Wang Y, et al. Compressive-sensing-based structure identification for multilayer networks. IEEE Trans Cybern, 2018, 48: 754–764

    Article  Google Scholar 

  10. Mei G, Wu X, Ning D, et al. Finite-time stabilization of complex dynamical networks via optimal control. Complexity, 2016, 21: 417–425

    Article  MathSciNet  Google Scholar 

  11. Wei X, Wu X, Chen S, et al. Cooperative epidemic spreading on a two-layered interconnected network. SIAM J Appl Dyn Syst, 2018, 17: 1503–1520

    Article  MathSciNet  MATH  Google Scholar 

  12. Wang J, Feng J, Xu C, et al. The synchronization of instantaneously coupled harmonic oscillators using sampled data with measurement noise. Automatica, 2016, 66: 155–162

    Article  MathSciNet  MATH  Google Scholar 

  13. Niu R, Wu X, Lu J, et al. Phase synchronization on spatially embedded duplex networks with total cost constraint. Chaos, 2018, 28: 093101

    Article  MathSciNet  Google Scholar 

  14. Li N, Wu X, Feng J, et al. Fixed-time synchronization of coupled neural networks with discontinuous activation and mismatched parameters. IEEE Trans Neural Netw Learning Syst, 2021, 32: 2470–2482

    Article  MathSciNet  Google Scholar 

  15. Zhou Q, Zhao S, Li H, et al. Adaptive neural network tracking control for robotic manipulators with dead zone. IEEE Trans Neural Netw Learning Syst, 2019, 30: 3611–3620

    Article  MathSciNet  Google Scholar 

  16. Holme P, Saramäki J. Temporal networks. Phys Rep, 2012, 519: 97–125

    Article  Google Scholar 

  17. Lu J H, Chen G R. A time-varying complex dynamical network model and its controlled synchronization criteria. IEEE Trans Automat Contr, 2005, 50: 841–846

    Article  MathSciNet  MATH  Google Scholar 

  18. Kohar V, Ji P, Choudhary A, et al. Synchronization in time-varying networks. Phys Rev E, 2014, 90: 022812

    Article  Google Scholar 

  19. Rakshit S, Majhi S, Bera B K, et al. Time-varying multiplex network: Intralayer and interlayer synchronization. Phys Rev E, 2017, 96: 062308

    Article  Google Scholar 

  20. Rakshit S, Bera B K, Ghosh D, et al. Emergence of synchronization and regularity in firing patterns in time-varying neural hypernetworks. Phys Rev E, 2018, 97: 052304

    Article  Google Scholar 

  21. Boccaletti S, Bianconi G, Criado R, et al. The structure and dynamics of multilayer networks. Phys Rep, 2014, 544: 1–122

    Article  MathSciNet  Google Scholar 

  22. Dwivedi S K, Baptista M S, Jalan S. Optimization of synchronizability in multiplex networks by rewiring one layer. Phys Rev E, 2017, 95: 040301

    Article  Google Scholar 

  23. Dwivedi S K, Sarkar C, Jalan S. Optimization of synchronizability in multiplex networks. Europhys Lett, 2015, 111: 10005

    Article  Google Scholar 

  24. Yang T, Meng Z, Shi G, et al. Network synchronization with nonlinear dynamics and switching interactions. IEEE Trans Automat Contr, 2016, 61: 3103–3108

    Article  MathSciNet  MATH  Google Scholar 

  25. Chen Y, Yu W, Tan S, et al. Synchronizing nonlinear complex networks via switching disconnected topology. Automatica, 2016, 70: 189–194

    Article  MathSciNet  MATH  Google Scholar 

  26. Hagberg A, Schult D A. Exploring network structure, dynamics, and function using network X. Chaos, 2018, 18: 037105

    Article  Google Scholar 

  27. Wei J, Wu X, Lu J A, et al. Synchronizability of duplex regular networks. Europhys Lett, 2017, 120: 20005

    Article  Google Scholar 

  28. Wei X, Emenheiser J, Wu X, et al. Maximizing synchronizability of duplex networks. Chaos, 2018, 28: 013110

    Article  MathSciNet  Google Scholar 

  29. Li Y, Wu X, Lu J, et al. Synchronizability of duplex networks. IEEE Trans Circuits Syst II, 2016, 63: 206–210

    Article  Google Scholar 

  30. Pecora L M, Carroll T L. Master stability functions for synchronized coupled systems. Phys Rev Lett, 1998, 80: 2109–2112

    Article  Google Scholar 

  31. Tang L, Wu X, Lu J, et al. Master stability functions for complete, intralayer, and interlayer synchronization in multiplex networks of coupled Rössler oscillators. Phys Rev E, 2019, 99: 012304

    Article  Google Scholar 

  32. So P, Cotton B C, Barreto E. Synchronization in interacting populations of heterogeneous oscillators with time-varying coupling. Chaos, 2008, 18: 037114

    Article  MathSciNet  MATH  Google Scholar 

  33. Watts D J, Strogatz S H. Collective dynamics of ‘small-world’ networks. Nature, 1998, 393: 440–442

    Article  MATH  Google Scholar 

  34. Erdös P, Rényi A. On random graphs. I. Publicationes mathematicae, 1959, 6: 290–297

    MathSciNet  MATH  Google Scholar 

  35. Barabási A L, Albert R. Emergence of scaling in random networks. Science, 1999, 286: 509–512

    Article  MathSciNet  MATH  Google Scholar 

  36. Barabási A L, Albert R, Jeong H. Mean-field theory for scale-free random networks. Physica A-Statistical Mech its Appl, 1999, 272: 173–187

    Article  Google Scholar 

  37. Barahona M, Pecora L M. Synchronization in small-world systems. Phys Rev Lett, 2002, 89: 054101

    Article  Google Scholar 

  38. Wang X F, Chen G R. Synchronization in scale-free dynamical networks: Robustness and fragility. IEEE Trans Circuits Syst I, 2002, 49: 54–62

    Article  MathSciNet  MATH  Google Scholar 

  39. Wang X F, Chen G R. Small-world, scale-free and beyond. IEEE Circuits Syst Magaz, 2003, 3: 6–20

    Article  Google Scholar 

  40. Rössler O E. An equation for continuous chaos. Phys Lett A, 1976, 57: 397–398

    Article  MATH  Google Scholar 

  41. Huang L, Chen Q, Lai Y C, et al. Generic behavior of master-stability functions in coupled nonlinear dynamical systems. Phys Rev E, 2009, 80: 036204

    Article  Google Scholar 

  42. Chen J, Lu J A, Zhan C J, et al. Laplacian Spectra and Synchronization Processes on Complex Networks. In: Thai M. Pardalos P, eds. Handbook of Optimization in Complex Networks. Springer Optimization and Its Applications, vol 57. Boston: Springer, 2012

    Chapter  Google Scholar 

  43. Newman M E J, Strogatz S H, Watts D J. Random graphs with arbitrary degree distributions and their applications. Phys Rev E, 2001, 64: 026118

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Mathematics and Statistics, Wuhan University, Wuhan, 430072, China

    XiaoQun Wu, Xiong Zhou & QiRui Yang

  2. Hubei Key Laboratory of Computational Science, Wuhan University, Wuhan, 430072, China

    XiaoQun Wu

  3. Research Centre of Nonlinear Science, Wuhan Textile University, Wuhan, 430073, China

    Jie Liu

  4. School of Journalism and Communication, Hubei University of Economics, Wuhan, 430205, China

    YuanYuan Chen

Authors
  1. XiaoQun Wu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Xiong Zhou
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Jie Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. QiRui Yang
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. YuanYuan Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding authors

Correspondence to QiRui Yang or YuanYuan Chen.

Additional information

This work was supported by the National Key Research and Development Program of China (Grant No. 2018AAA0101100), the National Natural Science Foundation of China (Grant No. 61973241), and the Natural Science Foundation of Hubei Province (Grant No. 2019CFA007).

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Wu, X., Zhou, X., Liu, J. et al. Synchronizability of time-varying structured duplex dynamical networks with different intra-layer rewiring mechanisms. Sci. China Technol. Sci. 65, 375–385 (2022). https://doi.org/10.1007/s11431-020-1807-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11431-020-1807-3

Search

Navigation