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Discrete Dynamics in Nature and Society
Volume 2014, Article ID 254749, 7 pages
http://dx.doi.org/10.1155/2014/254749
Research Article

Cluster Anticonsensus of Multiagent Systems Based on the -Theory

School of Mathematics, Yancheng Teachers University, Yancheng 224002, China

Received 13 October 2013; Accepted 8 February 2014; Published 9 April 2014

Academic Editor: Gualberto Solís-Perales

Copyright © 2014 Liping Zhang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. T. Vicsek, A. Czirk, E. Ben-Jacob, I. Cohen, and O. Shochet, “Novel type of phase transition in a system of self-driven particles,” Physical Review Letters, vol. 75, no. 6, pp. 1226–1229, 1995. View at Publisher · View at Google Scholar · View at Scopus
  2. A. Jadbabaie, J. Lin, and A. S. Morse, “Coordination of groups of mobile autonomous agents using nearest neighbor rules,” IEEE Transactions on Automatic Control, vol. 48, no. 6, pp. 988–1001, 2003. View at Publisher · View at Google Scholar · View at MathSciNet
  3. J. A. Fax and R. M. Murray, “Information flow and cooperative control of vehicle formations,” IEEE Transactions on Automatic Control, vol. 49, no. 9, pp. 1465–1476, 2004. View at Publisher · View at Google Scholar · View at MathSciNet
  4. A. V. Savkin, “Coordinated collective motion of groups of autonomous mobile robots: analysis of Vicsek's model,” IEEE Transactions on Automatic Control, vol. 49, no. 6, pp. 981–983, 2004. View at Publisher · View at Google Scholar · View at MathSciNet
  5. R. Olfati-Saber and R. M. Murray, “Consensus problems in networks of agents with switching topology and time-delays,” IEEE Transactions on Automatic Control, vol. 49, no. 9, pp. 1520–1533, 2004. View at Publisher · View at Google Scholar · View at MathSciNet
  6. R. Olfati-Saber, J. A. Fax, and R. M. Murray, “Consensus and cooperation in networked multi-agent systems,” Proceedings of the IEEE, vol. 95, no. 1, pp. 215–233, 2007. View at Publisher · View at Google Scholar · View at Scopus
  7. W. Ren and R. W. Beard, “Consensus seeking in multiagent systems under dynamically changing interaction topologies,” IEEE Transactions on Automatic Control, vol. 50, no. 5, pp. 655–661, 2005. View at Publisher · View at Google Scholar · View at MathSciNet
  8. Y.-P. Tian and C.-L. Liu, “Consensus of multi-agent systems with diverse input and communication delays,” IEEE Transactions on Automatic Control, vol. 53, no. 9, pp. 2122–2128, 2008. View at Publisher · View at Google Scholar · View at MathSciNet
  9. J. Zhu, Y.-P. Tian, and J. Kuang, “On the general consensus protocol of multi-agent systems with double-integrator dynamics,” Linear Algebra and Its Applications, vol. 431, no. 5-7, pp. 701–715, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. Y. Zhang and Y.-P. Tian, “Consentability and protocol design of multi-agent systems with stochastic switching topology,” Automatica, vol. 45, no. 5, pp. 1195–1201, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  11. M. Huang and J. H. Manton, “Coordination and consensus of networked agents with noisy measurements: stochastic algorithms and asymptotic behavior,” SIAM Journal on Control and Optimization, vol. 48, no. 1, pp. 134–161, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  12. X. Liu, T. Chen, and W. Lu, “Consensus problem in directed networks of multi-agents via nonlinear protocols,” Physics Letters A, vol. 373, no. 35, pp. 3122–3127, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  13. P. DeLellis, M. diBernardo, F. Garofalo, and D. Liuzza, “Analysis and stability of consensus in networked control systems,” Applied Mathematics and Computation, vol. 217, no. 3, pp. 988–1000, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  14. H. Jiang, J. Yu, and C. Zhou, “Consensus of multi-agent linear dynamic systems via impulsive control protocols,” International Journal of Systems Science, vol. 42, no. 6, pp. 967–976, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  15. H. Jiang and Q. Bi, “Impulsive synchronization of networked nonlinear dynamical systems,” Physics Letters A, vol. 374, no. 27, pp. 2723–2729, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  16. S. Zheng, G. Dong, and Q. Bi, “Impulsive synchronization of complex networks with non-delayed and delayed coupling,” Physics Letters A, vol. 373, no. 46, pp. 4255–4259, 2009. View at Publisher · View at Google Scholar · View at Scopus
  17. H. B. Jiang, “Hybrid adaptive and impulsive synchronisation of uncertain complex dynamical networks by the generalised Barbalat's lemma,” IET Control Theory and Applications, vol. 3, no. 10, pp. 1330–1340, 2009. View at Publisher · View at Google Scholar · View at MathSciNet
  18. L. Zhang, H. Jiang, and Q. Bi, “Reliable impulsive lag synchronization for a class of nonlinear discrete chaotic systems,” Nonlinear Dynamics, vol. 59, no. 4, pp. 529–534, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  19. C.-M. Kim, S. Rim, W.-H. Kye, J.-W. Ryu, and Y.-J. Park, “Anti-synchronization of chaotic oscillators,” Physics Letters A, vol. 320, no. 1, pp. 39–46, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  20. Y. Zhang and J. Sun, “Chaotic synchronization and anti-synchronization based on suitable separation,” Physics Letters A, vol. 330, no. 6, pp. 442–447, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  21. J. Hu, S. Chen, and L. Chen, “Adaptive control for anti-synchronization of Chua's chaotic system,” Physics Letters A, vol. 339, no. 6, pp. 455–460, 2005. View at Publisher · View at Google Scholar · View at Scopus
  22. J. Feng, Z. Tang, J. Wang, and Y. Zhao, “Pinning two nonlinearly coupled complex networks with an asymmetrical coupling matrix,” Discrete Dynamics in Nature and Society, vol. 2013, Article ID 959368, 11 pages, 2013. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  23. X. B. Lu and B. Z. Qin, “Adaptive cluster synchronization in complex dynamical networks,” Physics Letters A, vol. 373, no. 40, pp. 3650–3658, 2009. View at Publisher · View at Google Scholar · View at Scopus
  24. W. Lu, B. Liu, and T. Chen, “Cluster synchronization in networks of coupled nonidentical dynamical systems,” Chaos, vol. 20, no. 1, Article ID 013120, 12 pages, 2010. View at Publisher · View at Google Scholar · View at MathSciNet
  25. K. Czolczynski, P. Perlikowski, A. Stefanski, and T. Kapitaniak, “Clustering and synchronization of n Huygens' clocks,” Physica A, vol. 388, pp. 5013–5023, 2009. View at Google Scholar
  26. D. Cvetković, “Signless Laplacians and line graphs,” Bulletin, Classe des Sciences Mathématiques et Naturelles. Sciences Mathématiques, no. 30, pp. 85–92, 2005. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  27. D. Cvetković, P. Rowlinson, and S. K. Simić, “Signless Laplacians of finite graphs,” Linear Algebra and Its Applications, vol. 423, no. 1, pp. 155–171, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  28. D. Cvetković and S. K. Simić, “Towards a spectral theory of graphs based on the signless Laplacian. I,” Publications de l'Institut Mathématique, vol. 85(99), pp. 19–33, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  29. D. Cvetković and S. K. Simić, “Towards a spectral theory of graphs based on the signless Laplacian. II,” Linear Algebra and Its Applications, vol. 432, no. 9, pp. 2257–2272, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  30. D. Cvetković and S. K. Simić, “Towards a spectral theory of graphs based on the signless Laplacian. III,” Applicable Analysis and Discrete Mathematics, vol. 4, no. 1, pp. 156–166, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  31. C. S. Oliveira, L. S. de Lima, N. M. M. de Abreu, and P. Hansen, “Bounds on the index of the signless Laplacian of a graph,” Discrete Applied Mathematics, vol. 158, no. 4, pp. 355–360, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  32. P. Zhang, J. L. Wang, X. J. Li, M. H. Li, Z. R. Di, and Y. Fan, “Clustering coefficient and community structure of bipartite networks,” Physica A, vol. 387, pp. 6869–6875, 2008. View at Google Scholar
  33. L. Zhang and H. Jiang, “Impulsive cluster anticonsensus of discrete multiagent linear dynamic systems,” Discrete Dynamics in Nature and Society, vol. 2012, Article ID 857561, 11 pages, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  34. C. Godsil and G. Royle, Algebraic Graph Theory, vol. 207 of Graduate Texts in Mathematics, Springer, New York, NY, USA, 2001. View at Publisher · View at Google Scholar · View at MathSciNet
  35. J. P. LaSalle, The Stability of Dynamical Systems, SIAM, Philadelphia, Pa, USA, 1976. View at MathSciNet