Table of Contents Author Guidelines Submit a Manuscript
Mathematical Problems in Engineering
Volume 2011 (2011), Article ID 735248, 13 pages
http://dx.doi.org/10.1155/2011/735248
Research Article

Collective Dynamics of Swarms with a New Attraction/Repulsion Function

1Department of Mathematics and Physics, Beijing Institute of Petrochemical Technology, Beijing 102617, China
2State Key Laboratory of Turbulence and Complex Systems, Center for Systems and Control, College of Engineering, Peking University, Beijing 100871, China
3School of Electrical and Electronics Engineering, East China Jiaotong University, Nanchang 330013, China

Received 10 March 2011; Accepted 19 June 2011

Academic Editor: Jitao Sun

Copyright © 2011 Hong Shi and Guangming Xie. 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. D. W. Stephens and J. R. Krebs, Foraging Theory, Princeton University Press, Princeton, NJ, USA, 1986.
  2. J. Krause and G. Ruxton, Living in Groups, Oxford University Press, Oxford, UK, 2002.
  3. I. D. Couzin and J. Krause, “Self-organization and collective behavior in vertebrates,” Advances in the Study of Behavior, vol. 32, pp. 1–75, 2003. View at Publisher · View at Google Scholar · View at Scopus
  4. K. M. Passino, “Biomimicry of bacterial foraging for distributed optimization and control,” IEEE Control Systems Magazine, vol. 22, no. 3, pp. 52–67, 2002. View at Publisher · View at Google Scholar · View at Scopus
  5. E. Boabeau, M. Dorigo, and G. Theraulaz, Swarm Intelligence: From Natural to Artificial Systems, Oxford University Press, Oxford, UK, 1999.
  6. A. Czirók and T. Vicsek, “Collective behavior of interacting self-propelled particles,” Physica A: Statistical Mechanics and its Applications, vol. 281, no. 1, pp. 17–29, 2000. View at Publisher · View at Google Scholar · View at Scopus
  7. I. D. Couzin, J. Krause, N. R. Franks, and S. A. Levin, “Effective leadership and decision-making in animal groups on the move,” Nature, vol. 433, no. 7025, pp. 513–516, 2005. View at Publisher · View at Google Scholar · View at PubMed · View at Scopus
  8. G. Grégoire, H. Chaté, and Y. Tu, “Moving and staying together without a leader,” Physica D. Nonlinear Phenomena, vol. 181, no. 3-4, pp. 157–170, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. V. Gazi and K. M. Passino, “Stability analysis of swarms,” IEEE Transactions on Automatic Control, vol. 48, no. 4, pp. 692–697, 2003. View at Publisher · View at Google Scholar · View at MathSciNet
  10. V. Gazi and K. M. Passino, “Stability analysis of social foraging swarms,” IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics, vol. 34, no. 1, pp. 539–557, 2004. View at Publisher · View at Google Scholar · View at Scopus
  11. V. Gazi and K. M. Passino, “A class of attractions/repulsion functions for stable swarm aggregations,” International Journal of Control, vol. 77, no. 18, pp. 1567–1579, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  12. T. Chu, L. Wang, T. Chen, and S. Mu, “Complex emergent dynamics of anisotropic swarms: convergence vs oscillation,” Chaos, Solitons and Fractals, vol. 30, no. 4, pp. 875–885, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  13. L. Wang, H. Shi, T. Chu, W. Zhang, and L. Zhang, “Aggregation of foraging swarms,” in Lecture Notes in Artificial Intelligence, vol. 3339, pp. 766–777, Springer, Berlin, Germany, 2004. View at Publisher · View at Google Scholar
  14. H. Shi, L. Wang, T. Chu, and F. Xiao, “Self-organization of general multi-agent systems with complex interactions,” in Proceedings of the IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS '06), pp. 3203–3208, October 2006. View at Publisher · View at Google Scholar
  15. H. Shi, L. Wang, T. Chu, and M. Xu, “Collective dynamic behavior of anisotropic foraging swarms,” in Proceedings of the American Control Conference (ACC '07), pp. 2563–2568, July 2007. View at Publisher · View at Google Scholar
  16. B. Liu, T. G. Chu, L. Wang, and Z. F. Wang, “Swarm dynamics of a group of mobile autonomous agents,” Chinese Physics Letters, vol. 22, no. 1, pp. 254–257, 2005. View at Publisher · View at Google Scholar · View at Scopus
  17. H. G. Tanner, A. Jadbabaie, and G. J. Pappas, “Flocking in fixed and switching networks,” IEEE Transactions on Automatic Control, vol. 52, no. 5, pp. 863–868, 2007. View at Publisher · View at Google Scholar · View at MathSciNet
  18. R. Olfati-Saber, “Flocking for multi-agent dynamic systems: algorithms and theory,” IEEE Transactions on Automatic Control, vol. 51, no. 3, pp. 401–420, 2006. View at Publisher · View at Google Scholar · View at MathSciNet
  19. H. Shi, L. Wang, and T. Chu, “Virtual leader approach to coordinated control of multiple mobile agents with asymmetric interactions,” Physica D. Nonlinear Phenomena, vol. 213, no. 1, pp. 51–65, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  20. Y. Hong, J. Hu, and L. Gao, “Tracking control for multi-agent consensus with an active leader and variable topology,” Automatica, vol. 42, no. 7, pp. 1177–1182, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  21. H. Shi, L. Wang, and T. Chu, “Flocking of multi-agent systems with a dynamic virtual leader,” International Journal of Control, vol. 82, no. 1, pp. 43–58, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  22. G. Xie and L. Wang, “Moving formation convergence of a group of mobile robots via decentralised information feedback,” International Journal of Systems Science, vol. 40, no. 10, pp. 1019–1027, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  23. G. Xie and L. Wang, “Consensus control for a class of networks of dynamic agents,” International Journal of Robust and Nonlinear Control, vol. 17, no. 10-11, pp. 941–959, 2007. View at Publisher · View at Google Scholar
  24. F. Xiao and L. Wang, “Asynchronous consensus in continuous-time multi-agent systems with switching topology and time-varying delays,” IEEE Transactions on Automatic Control, vol. 53, no. 8, pp. 1804–1816, 2008. View at Publisher · View at Google Scholar