Convergence speed of consensus problems over undirected scale-free networks

Scale-free networks and consensus behaviour among multiple agents have both attracted much attention. To investigate the consensus speed over scale-free networks is the major topic of the present work. A novel method is developed to construct scale-free networks due to their remarkable power-law degree distributions, while preserving the diversity of network topologies. The time cost or iterations for networks to reach a certain level of consensus is discussed, considering the in∞uence from power-law parameters. They are both demonstrated to be reversed power-law functions of the algebraic connectivity, which is viewed as a measurement on convergence speed of the consensus behaviour. The attempts of tuning power-law parameters may speed up the consensus procedure, but it could also make the network less robust over time delay at the same time. Large scale of simulations are supportive to the conclusions.

[1]  Guanrong Chen,et al.  Universal robustness characteristic of weighted networks against cascading failure. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

[2]  Wang Bing-Hong,et al.  Opinion Spreading with Mobility on Scale-Free Networks ⁄ , 2008 .

[3]  Ying-Cheng Lai,et al.  Attack vulnerability of scale-free networks due to cascading breakdown. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[4]  Xiaofan Wang,et al.  On synchronization in scale-free dynamical networks , 2005 .

[5]  Guanrong Chen,et al.  Optimal weighting scheme for suppressing cascades and traffic congestion in complex networks. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.

[6]  Michael Mitzenmacher,et al.  Editorial: The Future of Power Law Research , 2005, Internet Math..

[7]  Ravi Kumar,et al.  Trawling the Web for Emerging Cyber-Communities , 1999, Comput. Networks.

[8]  Marc Schoenauer,et al.  On the evolution of scale-free topologies with a gene regulatory network model , 2009, Biosyst..

[9]  Bo Hu,et al.  General dynamics of topology and traffic on weighted technological networks. , 2005, Physical review letters.

[10]  Ying-Cheng Lai,et al.  Signatures of small-world and scale-free properties in large computer programs , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[11]  Naomi Ehrich Leonard,et al.  Proceedings Of The 2000 American Control Conference , 2000, Proceedings of the 2000 American Control Conference. ACC (IEEE Cat. No.00CH36334).

[12]  Y. Moreno,et al.  Disease spreading in structured scale-free networks , 2002, cond-mat/0210362.

[13]  Jurgen Kurths,et al.  Synchronization in complex networks , 2008, 0805.2976.

[14]  Li Shuang,et al.  A simple method to simultaneously achieve synchronization and anti-synchronization in chaotic systems , 2010 .

[15]  Chavdar Dangalchev,et al.  Generation models for scale-free networks , 2004 .

[16]  Reuven Cohen,et al.  Tolerance of scale-free networks: from friendly to intentional attack strategies , 2004 .

[17]  Walter Willinger,et al.  Towards a Theory of Scale-Free Graphs: Definition, Properties, and Implications , 2005, Internet Math..

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

[19]  A. Motter,et al.  Ensemble averageability in network spectra. , 2007, Physical review letters.

[20]  张丽萍,et al.  Reliable impulsive synchronization for a class of nonlinear chaotic systems , 2010 .

[21]  Alessandro Vespignani,et al.  Epidemic spreading in scale-free networks. , 2000, Physical review letters.

[22]  Richard M. Murray,et al.  Consensus problems in networks of agents with switching topology and time-delays , 2004, IEEE Transactions on Automatic Control.

[23]  Qi Wei,et al.  Improving consensual performance of multi-agent systems in weighted scale-free networks , 2009 .

[24]  Xu Wei,et al.  Complete synchronization of uncertain chaotic dynamical network via a simple adaptive control , 2008 .

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

[26]  Yangquan Chen,et al.  Experimental Validation of Consensus Algorithms for Multivehicle Cooperative Control , 2008, IEEE Transactions on Control Systems Technology.

[27]  Jing Zhou,et al.  Convergence speed in distributed consensus over dynamically switching random networks , 2009, Autom..

[28]  Liu Xingyuan,et al.  A novel evolving scale-free model with tunable attractiveness , 2010 .

[29]  Long Wang,et al.  Asynchronous Consensus in Continuous-Time Multi-Agent Systems With Switching Topology and Time-Varying Delays , 2006, IEEE Transactions on Automatic Control.

[30]  Mark E. J. Newman,et al.  Power-Law Distributions in Empirical Data , 2007, SIAM Rev..

[31]  Z. Neda,et al.  Networks in life: Scaling properties and eigenvalue spectra , 2002, cond-mat/0303106.

[32]  Hui-jun Sun,et al.  Cascade and breakdown in scale-free networks with community structure. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[33]  Yan-Bo Xie,et al.  Time-cumulative scale-free networks without both growth and preferential attachment , 2007 .

[34]  F. Atay,et al.  Network synchronization: Spectral versus statistical properties , 2006, 0706.3069.

[35]  Albert-László Barabási,et al.  Scale-Free Networks: A Decade and Beyond , 2009, Science.

[36]  M. Fiedler.  Algebraic connectivity of graphs , 1973 .

[37]  Suhan Ree,et al.  Generation of scale-free networks using a simple preferential-rewiring dynamics , 2007 .

[38]  Stephen P. Boyd,et al.  Fast linear iterations for distributed averaging , 2003, 42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475).