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Dynamic survivability of two-layer networks with different topologies

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Abstract

In light of the paramount importance of addressing safety concerns in dynamic network systems, this paper investigates the dynamic survivability of two-layer networks, thereby surpassing previous studies that predominantly focused on static or dynamic single-layer networks. An improved model is constructed with globally and Barabási–Albert scale-free coupled topologies under different interlayer couplings, and dynamic survivability is analyzed under different attack strategies. Our results suggest that intralayer coupling reduces dynamic survivability, while interlayer coupling exhibits the opposite effect. Furthermore, the intralayer coupling plays a crucial role in dynamic survivability of two-layer networks. The Barabási–Albert scale-free two-layer networks exhibit high survivability against random attack, yet demonstrate low survivability to deliberate attack. In the case of interlayer couplings, negative coupling has the greatest effect on dynamic survivability, while positive coupling has the least. These findings could provide new methods to explain the phenomena of dynamic networks and design survivable networks to prevent attack.

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Data Availability Statement

The data that support the findings of this study are available within the article.

References

  1. H. Frank, Survivability analysis of command and control communications networks-Part I. IEEE Trans. Commun. 22(5), 589–595 (1974). https://doi.org/10.1109/TCOM.1974.1092265

    Article  ADS  Google Scholar 

  2. B.A. Hollway, P.G. Neumann, Survivable Computer-Communication Systems: The Problem and Working Group Recommendations (US Army Research Laboratory, Washington, 1993)

    Google Scholar 

  3. Y. Zhu, J. Yan, Y. Tang, Y. Sun, H. He, Resilience analysis of power grids under the sequential attack. IEEE Trans. Inf. Forensics Secur. 9(12), 2340–2354 (2014). https://doi.org/10.1109/TIFS.2014.2363786

    Article  Google Scholar 

  4. J.W. Simpson-Porco, F. Dörfler, F. Bullo, Voltage collapse in complex power grids. Nat. Commun. 7(1), 10790 (2016). https://doi.org/10.1038/ncomms10790

    Article  ADS  Google Scholar 

  5. I. Tutanescu, E. Sofron, M. Ali, Security of internet-connected computer networks. Int. J. Internet Technol. Secur. Trans. 2(1–2), 109–121 (2010). https://doi.org/10.1504/IJITST.2010.031474

    Article  Google Scholar 

  6. R.J. Ellison, R.C. Linger, T. Longstaff, N.R. Mead, Survivable network system analysis: a case study. IEEE Softw. 16(4), 70–77 (1999). https://doi.org/10.1109/52.776952

    Article  Google Scholar 

  7. R.J. Ellison, C. Woody, Survivability Analysis Framework (Carnegie Mellon University, Software Engineering Institute, Pittsburgh, 2010)

  8. P. Holme, B.J. Kim, C.N.Y. Yoon, S.K. Han, Attack vulnerability of complex networks. Phys. Rev. E 65(5), 056109 (2002). https://doi.org/10.1103/PhysRevE.65.056109

    Article  ADS  Google Scholar 

  9. M. Manzano, E. Calle, J. Ripoll, A.M. Fagertun, V. Torres-Padrosa, S. Pahwa, C. Scoglio, Epidemic and cascading survivability of complex networks, in 2014 6th International Workshop on Reliable Networks Design and Modeling (RNDM), Barcelona (IEEE, 2014), pp. 187–193. https://doi.org/10.1109/RNDM.2014.7014950

  10. Y. Yin, Q. Liu, C. Zhang, J. Zhou, Survivability analysis of weighted-edge attacks on complex networks with incomplete information. Physica A 531, 120957 (2019). https://doi.org/10.1016/j.physa.2019.04.193

    Article  Google Scholar 

  11. M. Ingale, S.M. Shekatkar, Resource dependency and survivability in complex networks. Phys. Rev. E 102(6), 062304 (2020). https://doi.org/10.1103/PhysRevE.102.062304

    Article  ADS  MathSciNet  Google Scholar 

  12. P.K. Andersen, O. Borgan, R.D. Gill, N. Keiding, Statistical Models Based on Counting Processes (Springer, Berlin, 2012)

    Google Scholar 

  13. H. Binder, M. Schumacher, Allowing for mandatory covariates in boosting estimation of sparse high-dimensional survival models. BMC Bioinf. 9, 1–10 (2008). https://doi.org/10.1186/1471-2105-9-14

    Article  Google Scholar 

  14. P.D. Allison, Survival Analysis Using SAS: A Practical Guide (Sas Institute, Cary, 2010)

    Google Scholar 

  15. G. Yang, Y. Cai, C.K. Reddy, Spatio-temporal check-in time prediction with recurrent neural network based survival analysis, in Proceedings of the Twenty-Seventh International Joint Conference on Artificial Intelligence (2018)

  16. Y. Li, L. Wang, J. Wang, J. Ye, C.K. Reddy, Transfer learning for survival analysis via efficient l2, 1-norm regularized cox regression, in 2016 IEEE 16th International Conference on Data Mining (ICDM), Barcelona (IEEE, 2016), pp. 231–240. https://doi.org/10.1109/ICDM.2016.0034

  17. P. Wang, Y. Li, C.K. Reddy, Machine learning for survival analysis: a survey. ACM Comput. Surv. 51(6), 1–36 (2019). https://doi.org/10.1145/3214306

    Article  Google Scholar 

  18. S. Liu, Z. Sun, N. Zhao, W. Xu, Explosive transition in coupled oscillators through mixed attractive-repulsive interactions. Int. J. Bifurc. Chaos 32(02), 2250018 (2022). https://doi.org/10.1142/S0218127422500183

    Article  Google Scholar 

  19. S. Aghababaei, S. Balaraman, K. Rajagopal, F. Parastesh, S. Panahi, S. Jafari, Effects of autapse on the chimera state in a Hindmarsh-Rose neuronal network. Chaos Solitons Fractals 153, 111498 (2021). https://doi.org/10.1016/j.chaos.2021.111498

    Article  MathSciNet  Google Scholar 

  20. J. Li, H. Jiang, C. Hu, J. Yu, Analysis and discontinuous control for finite-time synchronization of delayed complex dynamical networks. Chaos Solitons Fractals 114, 291–305 (2018). https://doi.org/10.1016/j.chaos.2018.07.019

    Article  ADS  MathSciNet  Google Scholar 

  21. F. Hellmann, P. Schultz, C. Grabow, J. Heitzig, J. Kurths, Survivability of deterministic dynamical systems. Sci. Rep. 6(1), 29654 (2016). https://doi.org/10.1038/srep29654

    Article  ADS  Google Scholar 

  22. Z. Sun, Y. Wang, Dynamic survivability in oscillator systems. Phys. Scr. 98(9), 095208 (2023). https://doi.org/10.1088/1402-4896/aceadd

    Article  ADS  Google Scholar 

  23. Y. Wang, Z. Sun, S. Liu, Y. Zhou, W. Xu, Dynamic survivability in nonlinear oscillation systems with attractive-repulsive interaction. Int. J. Bifurc. Chaos 33(04), 2350049 (2023). https://doi.org/10.1142/S0218127423500499

    Article  MathSciNet  Google Scholar 

  24. I. Koulierakis, D.A. Verganelakis, I. Omelchenko, A. Zakharova, E. Schöll, A. Provata, Structural anomalies in brain networks induce dynamical pacemaker effects. Chaos 30(11), 113137 (2020). https://doi.org/10.1063/5.0006207

    Article  ADS  MathSciNet  Google Scholar 

  25. A. Clauset, C. Moore, M.E.J. Newman, Hierarchical structure and the prediction of missing links in networks. Nature 453(7191), 98–101 (2008). https://doi.org/10.1038/nature06830

    Article  ADS  Google Scholar 

  26. C. Luo, X. Wang, H. Liu, Controllability of time-delayed Boolean multiplex control networks under asynchronous stochastic update. Sci. Rep. 4(1), 1–10 (2014). https://doi.org/10.1038/srep07522

    Article  Google Scholar 

  27. M. Xu, J. Zhou, J. Lu, X. Wu, Synchronizability of two-layer networks. Eur. Phys. J. B 88(9), 1–6 (2015). https://doi.org/10.1140/epjb/e2015-60330-0

    Article  Google Scholar 

  28. X. Wei, X. Wu, J. Lu, J. Wei, J. Zhao, Y. Wang, Synchronizability of two-layer correlation networks. Chaos 31(10), 103124 (2021). https://doi.org/10.1063/5.0056482

    Article  ADS  MathSciNet  Google Scholar 

  29. L. Tang, J. Wang, J. Liang, Inter-layer synchronization on a two-layer network of unified chaotic systems: the role of network nodal dynamics. Chaos Solitons Fractals 174, 113887 (2023). https://doi.org/10.1016/j.chaos.2023.113887

    Article  MathSciNet  Google Scholar 

  30. Y. Liu, Z. Sun, X. Yang, W. Xu, Dynamical robustness and firing modes in multilayer memristive neural networks of nonidentical neurons. Appl. Math. Comput. 409, 126384 (2021). https://doi.org/10.1016/j.amc.2021.126384

    Article  MathSciNet  Google Scholar 

  31. Y. Liu, Z. Sun, X. Yang, W. Xu, Analysis of dynamical robustness of multilayer neuronal networks with inter-layer ephaptic coupling at different scales. Appl. Math. Modell. 112, 156–167 (2022). https://doi.org/10.1016/j.apm.2022.07.027

    Article  MathSciNet  Google Scholar 

  32. K. Morino, G. Tanaka, K. Aihara, Robustness of multilayer oscillator networks. Phys. Rev. E 83(5), 056208 (2011). https://doi.org/10.1103/PhysRevE.83.056208

    Article  ADS  Google Scholar 

Download references

Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant Nos. 11972288, 12272295). The authors would like to thank the anonymous referees for their efforts and valuable comments.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Northwestern Polytechnical University, 127 Youyi Xilu, Xi’an, 710072, Shaanxi, People’s Republic of China

    Yuexin Wang, Zhongkui Sun, Hanqi Zhang, Shutong Liu & Wei Xu

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  1. Yuexin Wang
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  2. Zhongkui Sun
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  3. Hanqi Zhang
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  4. Shutong Liu
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  5. Wei Xu
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Contributions

Yuexin Wang formulated the research idea, produced the results, analyzed the data and prepared plots along with studying and wrote the main text of the manuscript. Zhongkui Sun provided direction and guidance along the way and contributed to the final writing. Hanqi Zhang, Shutong Liu and Wei Xu contributed to checking the correctness of the results, improving the simulations and image presentation.

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Correspondence to Zhongkui Sun.

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Wang, Y., Sun, Z., Zhang, H. et al. Dynamic survivability of two-layer networks with different topologies. Eur. Phys. J. Plus 139, 94 (2024). https://doi.org/10.1140/epjp/s13360-024-04906-9

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