Mathematical Problems in Engineering
Volume 2011 (2011), Article ID 745257, 21 pages
Research Article

Analysis of the Emergence in Swarm Model Based on Largest Lyapunov Exponent

1Network and Computation Research Center, Chongqing University of Posts and Telecommunications, Chongqing 400065, China
2School of Engineering and Computing, Glasgow Caledonian University, Cowcaddens Road, Glasgow G4 0BA, UK

Received 6 January 2011; Accepted 20 June 2011

Academic Editor: Mohammad Younis

Copyright © 2011 Yu Wu 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.


Emergent behaviors of collective intelligence systems, exemplified by swarm model, have attracted broad interests in recent years. However, current research mostly stops at observational interpretations and qualitative descriptions of emergent phenomena and is essentially short of quantitative analysis and evaluation. In this paper, we conduct a quantitative study on the emergence of swarm model by using chaos analysis of complex dynamic systems. This helps to achieve a more exact understanding of emergent phenomena. In particular, we evaluate the emergent behaviors of swarm model quantitatively by using the chaos and stability analysis of swarm model based on largest Lyapunov exponent. It is concluded that swarm model is at the edge of chaos when emergence occurs, and whether chaotic or stable at the beginning, swarm model will converge to stability with the elapse of time along with interactions among agents.