1. Asymptotic Behavior and Collision Avoidance in the Cucker–Smale Model.
- Author
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Yin, Xiuxia, Yue, Dong, and Chen, Zili
- Subjects
- *
KINETIC energy , *BEHAVIOR , *MULTIAGENT systems , *WEIGHT measurement - Abstract
For the long-range-communicated Cucker–Smale (C–S) model, asymptotic flocking can be obtained by taking full use of a key equality about the kinetic energy. However, such behavior does not exist for the short-range-communicated C–S model with general initial data. In this note, we first establish a new equality about the second-order velocity-position moments for general C–S models. Then, we use this equality to deduce a new type of asymptotic behavior for the short-range-communicated C–S model. Such behavior not only reflects an essential feature of the short-range communication weight, but also has some potential applications in the complex multicluster problem. Besides, collision avoidance is also obtained for the C–S model with some singular short-range communication weights. [ABSTRACT FROM AUTHOR]
- Published
- 2020
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