Synchronization properties of interconnected network based on the vital node
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In this paper, we perform an intensive study of the synchronization properties of interconnected network and the concepts of vital node, and the simplest and equivalent network is firstly introduced. We strictly derive the eigenvalues of Laplacian matrix and the synchronizability of interconnected network and its simplest and equivalent network through utilizing the master stability function approach. Firstly, we find the synchronizability of interconnected network is identical to its simplest and equivalent network. Secondly, we identify the general factors that determine the synchronizability of interconnected network and further analyze the impact of different factors on the synchronizability. Finally, theoretical analysis and numerical simulations are carried out to indicate the validity and effectiveness of current analysis. The current results are beneficial to understand the dynamical behaviors of complex networked systems.
KeywordsSynchronization Interconnected network Vital node Simplest and equivalent network Eigenvalue analysis
This work was partially supported by the National Natural Science Foundation of China under Grant Nos. 61403280, 61374169 and 61773286. LW acknowledge the support from Excellent Young Teachers Program of Tianjin. LW, SWS and CYX acknowledge the support from 131 Innovative Talents Program of Tianjin. CYX also acknowledges the support from the Scientific Research Foundation for the Returned Overseas Chinese Scholars (Ministry of Education).
- 19.Chen, F., Ren, W.: A connection between dynamic region-following formation control and distributed average tracking. IEEE Trans. Cybern. 99, 1–13 (2017)Google Scholar
- 35.Wider, N., Garas, A., Scholtes, I., Schweitzer, F.: An ensemble perspective on multi-layer networks. Interconnected, Networks; pp. 37–59 (2016)Google Scholar
- 37.Xu, M.M., Lu, J.A., Zhou, J.: Synchronizability and eigenvalues of two-layer star networks. Acta Phys. Sinica 65(2), 028902 (2016)Google Scholar
- 39.The Algebra Group of Teaching and Research Section of Algebra and Gemotry, Mathematics Department, Beijing University 2003 Advanced Algebra, 3rd edn. p 4382. Higher Education Press, Beijing (in Chinese)Google Scholar