Paper Info
Title
A revisit to the consensus for linearized Vicsek model under joint rooted leadership via a special matrix.
Abstract
We address the exponential consensus problem for the linearized Vicsek model which was introduced by Jadbabaie et al. in [10] under a joint rooted leadership via the (sp) matrices. This model deals with self-propelled particles moving in the plane with the same speed but different headings interacting with neighboring agents by a linear relaxation rule. When the time- varying switching topology of the neighbor graph satisfies some weak connectivity condition, namely, "joint connectivity condition" in the spatial-temporal domain, it is well known that the consensus for the linearized Vicsek model can be achieved asymptotically. In this paper, we extend the theory of (sp) matrices and apply it to revisit this asymptotic consensus problem and give an explicit estimate on the maximum Lyapunov exponent, when the underlying network topology satisfies the joint rooted leadership which is directed and non-symmetric.
Year
DOI
Venue
2014
10.3934/nhm.2014.9.335
NETWORKS AND HETEROGENEOUS MEDIA
Keywords
Field
DocType
The Vicsek model,joint rooted leadership,consensus,(sp) matrix,maximum Lyapunov exponent
Consensus,Applied mathematics,Graph,Mathematical economics,Exponential function,Mathematical analysis,Matrix (mathematics),Network topology,Lyapunov exponent,Mathematics
Journal
Volume
Issue
ISSN
9
2
1556-1801
Citations 
PageRank 
References 
0
0.34
11
Authors
3
Name
Order
Citations
PageRank
Zhuchun Li131.07
Xiaoping Xue218617.00
Seung-Yeal Ha31615.87