Journal
PHYSICS LETTERS A
Volume 383, Issue 1, Pages 1-9Publisher
ELSEVIER SCIENCE BV
DOI: 10.1016/j.physleta.2018.09.010
Keywords
Stability; Swarm; Cohesion; Rooted leadership
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Funding
- Ministry of Science and Technology of Taiwan [MOST 105-2115-M-017-001]
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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. (C) 2018 Elsevier B.V. All rights reserved.
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