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ON THE CRITICAL EXPONENT FOR FLOCKS UNDER HIERARCHICAL LEADERSHIP.
- Source :
-
Mathematical Models & Methods in Applied Sciences . Aug2009 Supplement 1, Vol. 19, p1391-1404. 14p. - Publication Year :
- 2009
-
Abstract
- Very recently, a model for flocking was introduced by Cucker and Smale together with a proof of convergence. This proof established unconditional convergence to a common velocity provided the interaction between agents was strong enough and conditional convergence otherwise. The strength of the interaction is measured by a parameter β ≥ 0 and the critical value at which unconditional convergence stops holding is β = 1/2. This model was extended by Shen to allow for a hierarchical leadership structure among the agents and similar convergence results were proved. But, for discrete time, unconditional convergence was proved only for $\beta < \frac{1}{2k}$ (k being the number of agents). In this note we improve on this result showing that unconditional convergence holds indeed for β < 1/2. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 02182025
- Volume :
- 19
- Database :
- Academic Search Index
- Journal :
- Mathematical Models & Methods in Applied Sciences
- Publication Type :
- Academic Journal
- Accession number :
- 44270173
- Full Text :
- https://doi.org/10.1142/S0218202509003851