Synchronization Analysis of High Order Layered Complex Networks

Abstract

In this paper, high-order layered complex networks are proposed. The synchronization is discussed in detail. The relations of synchronization, individual coupling matrices and the intrinsic function of the uncoupled system are given. As special cases, the synchronization of monolayer networks and multiplex networks discussed in the literature can be obtained.

Keywords

High-order layered network / Linearly coupled systems / Synchronization / 93D20 / 34D06

References

[1] Delellis P, Bernardo M D, Russo G. On QUAD, Lipschitz, and contracting vector fields for consensus and synchronization of networks. IEEE Trans. Circuits Syst. I Regul. Pap., 2011, 58(3): 576-583

[2] Gao J, Buldyrev S V, Stanley H E, Havlin S. Networks formed from interdependent networks. Nat. Phys., 2012, 8: 40-48

[3] Lu W, Chen T. New approach to synchronization analysis of linearly coupled ordinary differential systems. Physica D, 2006, 213(2): 214-230

[4] Lu W, Chen T. QUAD-condition, synchronization, consensus of multiagents, and anti-synchronization of complex networks. IEEE Trans. Cybern., 2021, 51(6): 3384-3388

[5] Pecora L, Carroll T, Johnson Get al.. Synchronization stability in coupled oscillator arrays: solution for arbitrary configuration. Int. J. Bifurcat. Chaos, 2000, 10(2): 273-290

[6] Pecora L M, Carroll T L. Synchronization in chaotic systems. Phys. Rev. Lett., 1990, 64(8): 821-824

[7] Sevilla-Escoboza R, Sendiña-Nadal I, Leyva Iet al.. Inter-layer synchronization in multiplex networks of identical layers. Chaos, 2016, 26: 065304

[8] Wu C W, Chua L O. Synchronization in an array of linearly coupled dynamical systems. IEEE Trans. Circuits Syst. I. Fundam. Theory Appl., 1995, 42(8): 430-447

[9] Wu C W. Synchronization in networks of nonlinear dynamical systems coupled via a directed graph. Nonlinearity, 2005, 18(3): 1057-1064

[10] Wu D, Tang M, Liu Z, Lai Y. Impact of inter-layer hopping on epidemic spreading in a multilayer network. Commun. Nonlinear Sci. Numer. Simul., 2020, 90: 105403

[11] Deng Y, Jia Z, Deng G, Zhang Q. Eigenvalue spectrum and synchronizability of multiplex chain networks. Physica A, 2020, 537: 122631

[12] Khalaf A J M, Alsaadi F E, Alsaadi F Eet al.. Synchronization in a multiplex network of gene oscillators. Phys. Lett. A, 2019, 383(31): 125919

[13] Bera B K, Rakshit S, Ghosh D. Intralayer synchronization in neuronal multiplex network. Eur. Phys. J. Spec. Top., 2019, 228: 2441-2454

[14] Tang L, Wu X, Lü Jet al.. Master stability functions for complete, intra-layer and inter-layer synchronization in multiplex networks. Phys. Rev. E, 2019, 99: 012304

[15] Gómez S, Díaz-Guilera A, Gómez-Gardeñes Jet al.. Diffusion dynamics on multiplex networks. Phys. Rev. Lett., 2013, 110: 028701

[16] Xu M, Zhou J, Lu J, Wu X. Synchronizability of two-layer networks. Eur. Phys. J. B, 2015, 88: 240

[17] Chen T. Synchronization of multi-cluster complex networks. Neural Netw., 2022, 156: 239-243

RIGHTS & PERMISSIONS

The Editorial Office of CAM and Springer-Verlag Berlin Heidelberg