Paper Info
Title
Cucker--Smale Flocking under Rooted Leadership with Fixed and Switching Topologies
Abstract
In recent years, a number of articles have focused on mathematical models for emergent phenomena, for instance, the flocking of birds or the schooling of fish. In 2007, Cucker and Smale proposed an ingenious model which captures many of the observed features of moving animals. Subsequently, Shen extended the result to hierarchically structured flocks. Motivated by these works, in this paper we study the discrete Cucker-Smale flocking under rooted leadership, which means that there exists an overall leader such that any other agent is led, directly or indirectly, by the leader. The feature of our proposal, departing from the existing models, is that both the assumption of symmetry and the partial ordering of a hierarchy are dropped. The rooted leadership topology is a necessary condition for the group to converge towards a single leader's fixed constant velocity. The rates of convergence are established for flocks with fixed and switching topologies. The results may reveal the applicability and advantage of cooperation, or exchange of information, inside the group.
Year
DOI
Venue
2010
10.1137/100791774
SIAM JOURNAL ON APPLIED MATHEMATICS
Keywords
Field
DocType
Cucker-Smale flocking,rooted leadership,discrete-time system,directed graph,switched system
Convergence (routing),Flocking (texture),Mathematical optimization,Existential quantification,Directed graph,Network topology,Theoretical computer science,Hierarchy,Mathematical model,Partially ordered set,Mathematics
Journal
Volume
Issue
ISSN
70
8
0036-1399
Citations 
PageRank 
References 
7
0.56
2
Authors
2
Name
Order
Citations
PageRank
Zhuchun Li1165.00
Xiaoping Xue229517.54