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Flocking of a Cucker–Smale Type Model with Compactly Supported Interaction Functions.
- Source :
-
Acta Mathematica Sinica . Sep2024, Vol. 40 Issue 9, p2285-2296. 12p. - Publication Year :
- 2024
-
Abstract
- How to analyze flocking behaviors of a multi-agent system with local interaction functions is a challenging problem in theory. Motsch and Tadmor in 2011 also stressed the significance to assume that the interaction function is rapidly decaying or cut-off at a finite distance (cf. Motsch and Tadmor in J. Stat. Phys. 2011). In this paper, we study the flocking behavior of a Cucker–Smale type model with compactly supported interaction functions. Using properties of a connected stochastic matrix, together with an elaborate analysis on perturbations of a linearized system, we obtain a sufficient condition imposed only on model parameters and initial data to guarantee flocking. Moreover, it is shown that the system achieves flocking at an exponential rate. [ABSTRACT FROM AUTHOR]
- Subjects :
- *STOCHASTIC matrices
*NEIGHBORS
Subjects
Details
- Language :
- English
- ISSN :
- 14398516
- Volume :
- 40
- Issue :
- 9
- Database :
- Academic Search Index
- Journal :
- Acta Mathematica Sinica
- Publication Type :
- Academic Journal
- Accession number :
- 178969092
- Full Text :
- https://doi.org/10.1007/s10114-024-2127-0