Enhancing synchronizability by rewiring networks

According to different forms of synchronized region, complex networks are divided into type I (unbounded synchronization region) and type II (bounded synchronization region) networks. This paper presents a rewiring algorithm to enhance the synchronizability of type I and type II networks. By utilizing the algorithm for an unweighted and undirected network, a better synchronizability of network with the same number of nodes and edges can be obtained. Numerical simulations on several different network models are used to support the proposed procedure. The relationship between different topological properties of the networks and the number of rewirings are shown. It finds that the final optimized network is independent of the initial network, and becomes homogeneous. In addition the optimized networks have similar structural properties in the sense of degree, and node and edge betweenness centralities. However, they do not have similar cluster coefficients for type II networks. The research may be useful for designing more synchronizable networks and understanding the synchronization behaviour of networks.

[1]  R. Merris.  Laplacian graph eigenvectors , 1998 .

[2]  Johnson,et al.  Three coupled oscillators as a universal probe of synchronization stability in coupled oscillator arrays , 2000, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[3]  Ljupco Kocarev,et al.  Synchronization in power-law networks. , 2005, Chaos.

[4]  Sergio Barbarossa,et al.  Decentralized Maximum-Likelihood Estimation for Sensor Networks Composed of Nonlinearly Coupled Dynamical Systems , 2006, IEEE Transactions on Signal Processing.

[5]  S. N. Dorogovtsev,et al.  Evolution of networks , 2001, cond-mat/0106144.

[6]  Duncan J. Watts,et al.  Collective dynamics of ‘small-world’ networks , 1998, Nature.

[7]  Albert,et al.  Emergence of scaling in random networks , 1999, Science.

[8]  Mahdi Jalili,et al.  Enhancing synchronizability of weighted dynamical networks using betweenness centrality. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

[9]  M E J Newman,et al.  Community structure in social and biological networks , 2001, Proceedings of the National Academy of Sciences of the United States of America.

[10]  J. Gómez-Gardeñes,et al.  From scale-free to Erdos-Rényi networks. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[11]  Albert-László Barabási,et al.  Statistical mechanics of complex networks , 2001, ArXiv.

[12]  Zoltán Toroczkai,et al.  Suppressing Roughness of Virtual Times in Parallel Discrete-Event Simulations , 2003, Science.

[13]  S. Boccaletti,et al.  Synchronization is enhanced in weighted complex networks. , 2005, Physical review letters.

[14]  T. Carroll,et al.  Master Stability Functions for Synchronized Coupled Systems , 1998 .

[15]  A. Hagberg,et al.  Rewiring networks for synchronization. , 2008, Chaos.

[16]  R. Merris.  Laplacian matrices of graphs: a survey , 1994 .

[17]  Chen Guan-Rong,et al.  Pinning-controlled synchronization of complex networks with bounded or unbounded synchronized regions , 2009 .

[18]  Mahdi Jalili,et al.  Enhancing synchronizability of dynamical networks using the connection graph stability method , 2007, Int. J. Circuit Theory Appl..

[19]  M. Newman,et al.  Scientific collaboration networks. II. Shortest paths, weighted networks, and centrality. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[20]  Xiao Fan Wang,et al.  Synchronization in scale-free dynamical networks: robustness and fragility , 2001, cond-mat/0105014.

[21]  Leonard M. Freeman,et al.  A set of measures of centrality based upon betweenness , 1977 .

[22]  J. Kurths,et al.  Enhancing complex-network synchronization , 2004, cond-mat/0406207.

[23]  A. Schnitzler,et al.  Normal and pathological oscillatory communication in the brain , 2005, Nature Reviews Neuroscience.

[24]  Reza Olfati-Saber,et al.  Consensus and Cooperation in Networked Multi-Agent Systems , 2007, Proceedings of the IEEE.

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

[26]  Ying-Cheng Lai,et al.  Enhancing synchronization based on complex gradient networks. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[27]  M. A. Muñoz,et al.  Entangled networks, synchronization, and optimal network topology. , 2005, Physical review letters.

[28]  Mauricio Barahona,et al.  Synchronization in small-world systems. , 2002, Physical review letters.

[29]  M. Newman,et al.  Renormalization Group Analysis of the Small-World Network Model , 1999, cond-mat/9903357.

[30]  J. Kurths,et al.  Network synchronization, diffusion, and the paradox of heterogeneity. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[31]  M. A. Muñoz,et al.  Network synchronization: optimal and pessimal scale-free topologies , 2007, 0710.4886.

[32]  S. Jian,et al.  The study of a new n/p tunnel recombination junction and its application in a-Si:H/μc-Si:H tandem solar cells , 2009 .

[33]  D. Earn,et al.  Coherence and conservation. , 2000, Science.