Stability analysis of a swarm model with rooted leadership

In this paper, we consider the stability of a swarm model, which is typically associated with the phenomenon of maintaining cohesion. In the swarm model, each individual has its own intrinsic nonlinear dynamics and the interaction between individuals follows a rooted leadership topology. We prove th...

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Bibliographic Details
Published inPhysics letters. A Vol. 383; no. 1; pp. 1 - 9
Main Author Li, Chun-Hsien
Format Journal Article
LanguageEnglish
Published Elsevier B.V 05.01.2019
Subjects
Cohesion
Rooted leadership
Stability
Swarm
Swarm
Cohesion
Stability
Rooted leadership
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Summary:In this paper, we consider the stability of a swarm model, which is typically associated with the phenomenon of maintaining cohesion. In the swarm model, each individual has its own intrinsic nonlinear dynamics and the interaction between individuals follows a rooted leadership topology. We prove that, if the corresponding real symmetric matrix is negative definite, then the swarm is stable in the sense that all individuals will eventually form a cohesive swarm. In addition, we obtain the bounds of the swarm size. Numerical simulations were conducted to validate the theoretical results. •We study the stability of a swarm model, which is typically associated with the phenomenon of maintaining cohesion.•Each individual has its own dynamics and the interaction between individuals follows a rooted leadership structure.•Sufficient conditions that ensure the occurrence of swarm cohesion are proposed.
ISSN:0375-9601
1873-2429
DOI:10.1016/j.physleta.2018.09.010