Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



On the Cucker-Smale flocking with alternating leaders

Authors: Zhuchun Li and Seung-Yeal Ha
Journal: Quart. Appl. Math. 73 (2015), 693-709
MSC (2010): Primary 92D25; Secondary 92C42
DOI: https://doi.org/10.1090/qam/1401
Published electronically: September 11, 2015
MathSciNet review: 3432279
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Abstract: We discuss the emergent flocking behavior in a group of Cucker-Smale flocking agents under rooted leadership with alternating leaders. It is well known that the network topology regulates the emergent behaviors of flocks. All existing results on the Cucker-Smale model with leader-follower topologies assume a fixed leader during the temporal evolution process. The rooted leadership is the most general topology taking a leadership. Motivated by collective behaviors observed in the flocks of birds, swarming fishes and potential engineering applications, we consider the rooted leadership with alternating leaders; that is, at each time slice there is a leader, but it can be switched among the agents from time to time. We provide several sufficient conditions leading to the asymptotic flocking among the Cucker-Smale agents under rooted leadership with alternating leaders.

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Additional Information

Zhuchun Li
Affiliation: Department of Mathematics, Harbin Institute of Technology, Harbin 150001, People’s Republic of China
Email: lizhuchun@gmail.com

Seung-Yeal Ha
Affiliation: Department of Mathematical Sciences and Research Institute of Mathematics, Seoul National University, Seoul 151-747, Korea
Email: syha@snu.ac.kr

DOI: https://doi.org/10.1090/qam/1401
Keywords: Cucker-Smale agent, alternating leaders, rooted leadership, flocking
Received by editor(s): February 24, 2014
Received by editor(s) in revised form: March 14, 2014
Published electronically: September 11, 2015
Article copyright: © Copyright 2015 Brown University