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Complex emergent dynamics of anisotropic swarms: Convergence vs oscillation

Author

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  • Chu, Tianguang
  • Wang, Long
  • Chen, Tongwen
  • Mu, Shumei

Abstract

This paper considers an anisotropic swarm model with a simple attraction and repulsion function. It is shown that the members of a reciprocal swarm will aggregate and eventually form a cohesive cluster of finite size around the swarm center. Moreover, the swarm system is also completely stable, i.e., every solution converges to the set of equilibrium points of the system. These results are also valid for a class of non-reciprocal swarms under the detailed balance condition on coupling weights. For general non-reciprocal swarms, numerical simulations are worked out to demonstrate more complex oscillatory motions in the systems. The study provides further insight into the effect of the interaction pattern on the collective behavior of a swarm system.

Suggested Citation

  • Chu, Tianguang & Wang, Long & Chen, Tongwen & Mu, Shumei, 2006. "Complex emergent dynamics of anisotropic swarms: Convergence vs oscillation," Chaos, Solitons & Fractals, Elsevier, vol. 30(4), pages 875-885.
    • Handle: RePEc:eee:chsofr:v:30:y:2006:i:4:p:875-885
    DOI: 10.1016/j.chaos.2005.08.133
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    References listed on IDEAS

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    1. Mu, Shumei & Chu, Tianguang & Wang, Long, 2005. "Coordinated collective motion in a motile particle group with a leader," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 351(2), pages 211-226.
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    Cited by:

    1. Liu, Bo & Chu, Tianguang & Wang, Long & Wang, Zhanfeng, 2008. "Collective motion of a class of social foraging swarms," Chaos, Solitons & Fractals, Elsevier, vol. 38(1), pages 277-292.
    2. Wu, Jianxin & Chen, Qingfei & Hong, Yiguang, 2009. "Striped attractor generation and synchronization analysis for coupled Rössler systems," Chaos, Solitons & Fractals, Elsevier, vol. 39(1), pages 322-331.
    3. Zhifu Chen & Tianguang Chu, 2013. "Multi-agent system model with mixed coupling topologies for pattern formation and formation splitting," Mathematical and Computer Modelling of Dynamical Systems, Taylor & Francis Journals, vol. 19(4), pages 388-400.
    4. Hongwei Jia & Jun Zhao, 2016. "Output regulation of switched linear multi-agent systems: an agent-dependent average dwell time method," International Journal of Systems Science, Taylor & Francis Journals, vol. 47(11), pages 2510-2520, August.

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