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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 783279, 9 pages
Research Article

Cucker-Smale Flocking with Bounded Cohesive and Repulsive Forces

1School of Electronics and Information, Hangzhou Dianzi University, Hangzhou 310018, China
2School of Information Engineering, Huanghuai University, Henan 463000, China
3Department of Mathematics, Southeast University, Nanjing 210096, China
4Department of Mathematics, King Abdulaziz University, Jeddah 21589, Saudi Arabia
5School of Science, Linyi University, Linyi, Shandong 276005, China

Received 6 July 2013; Accepted 27 August 2013

Academic Editor: A. M. Elaiw

Copyright © 2013 Qiang Song 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.


This paper proposes two Cucker-Smale-type flocking models by introducing both cohesive and repulsive forces to second-order multiagent systems. Under some mild conditions on the initial state of the flocking system, it is shown that the velocity consensus of the agents can be reached independent of the parameter which describes the decay of communication rates. In particular, the collision between any two agents can always be avoided by designing an appropriate bounded repulsive function based on the initial energy of the flock. Numerical examples are given to demonstrate the effectiveness of the theoretical analysis.