Graph Comparison and Coupling Strength Allocation for Synchronization in Multiplex Networks

This paper is aimed at exploring the strength allocation strategy on multiplex network from the perspective of graph theory. Assuming the topology and the sum of strength are fixed, distributing couplings strength with different numerical value to enhance synchronizability. Compared with average distribution and degree distribution, allocation referred to graph comparison method is more comprehensive and high-performance. Numerical examples for physical multiplex network are also provided to confirm the effectiveness.

[1]  Xinzhi Liu,et al.  Fractional order Lyapunov stability theorem and its applications in synchronization of complex dynamical networks , 2014, Commun. Nonlinear Sci. Numer. Simul..

[2]  Complex Network Application in Fault Diagnosis of Analog Circuits , 2011, Int. J. Bifurc. Chaos.

[3]  Didier Colle,et al.  Power consumption modeling in optical multilayer networks , 2012, Photonic Network Communications.

[4]  Yang Li,et al.  Synchronizability of Duplex Networks , 2016, IEEE Transactions on Circuits and Systems II: Express Briefs.

[5]  M. Hasler,et al.  Connection Graph Stability Method for Synchronized Coupled Chaotic Systems , 2004 .

[6]  Z. Wang,et al.  The structure and dynamics of multilayer networks , 2014, Physics Reports.

[7]  R. F. Cancho,et al.  Topology of technology graphs: small world patterns in electronic circuits. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[8]  Ljupco Kocarev,et al.  On opinion formation and synchronization in multiplex networks , 2013, 2013 21st Telecommunications Forum Telfor (TELFOR).

[9]  Chai Wah Wu,et al.  Synchronization in Complex Networks of Nonlinear Dynamical Systems , 2008 .

[10]  M. Hasler,et al.  Synchronization in asymmetrically coupled networks with node balance. , 2006, Chaos.

[11]  D. Watts.  Networks, Dynamics, and the Small‐World Phenomenon1 , 1999, American Journal of Sociology.

[12]  S. Strogatz.  Exploring complex networks , 2001, Nature.

[13]  A. Díaz-Guilera,et al.  Replicator dynamics with diffusion on multiplex networks. , 2016, Physical review. E.

[14]  Ming Cao,et al.  Graph comparison and its application in network synchronization , 2013, 2013 European Control Conference (ECC).

[15]  Erik M. Bollt,et al.  Master stability functions for coupled nearly identical dynamical systems , 2008, 0811.0649.

[16]  C. K. Michael Tse,et al.  Synchronization in Directed Complex Networks Using Graph Comparison Tools , 2015, IEEE Transactions on Circuits and Systems I: Regular Papers.

[17]  Barbora Micenková,et al.  Combinatorial Analysis of Multiple Networks , 2013, ArXiv.

[18]  Xiaoqun Wu,et al.  Synchronizability of two-layer networks , 2015 .

[19]  Hui Liu,et al.  Coupling Strength Allocation for Synchronization in Complex Networks Using Spectral Graph Theory , 2014, IEEE Transactions on Circuits and Systems I: Regular Papers.

[20]  Minfang Peng,et al.  Global similarity tests of physical designs of circuits: A complex network approach , 2014, Appl. Math. Comput..

[21]  Conrado J. Pérez Vicente,et al.  Diffusion dynamics on multiplex networks , 2012, Physical review letters.

[22]  L. Chua,et al.  Synchronization in an array of linearly coupled dynamical systems , 1995 .

[23]  Mark E. J. Newman,et al.  The Structure and Function of Complex Networks , 2003, SIAM Rev..