Abstract
We present a non-trivial lower bound for the critical coupling strength to the Cucker-Smale model with unit speed constraint and short-range communication weight from the viewpoint of a mono-cluster(global) flocking. For a long-range communication weight, the critical coupling strength is zero in the sense that the mono-cluster flocking emerges from any initial configurations for any positive coupling strengths, whereas for a short-range communication weight, a mono-cluster flocking can emerge from an initial configuration only for a sufficiently large coupling strength. Our main interest lies on the condition of non-flocking. We provide a positive lower bound for the critical coupling strength. We also present numerical simulations for the upper and lower bounds for the critical coupling strength depending on initial configurations and compare them with analytical results.
| Original language | English |
|---|---|
| Pages (from-to) | 2763-2793 |
| Number of pages | 31 |
| Journal | Discrete and Continuous Dynamical Systems |
| Volume | 38 |
| Issue number | 6 |
| DOIs | |
| State | Published - Jun 2018 |
Bibliographical note
Funding Information:2010 Mathematics Subject Classification. Primary: 34D05; Secondary: 37C75, 92D50. Key words and phrases. Critical coupling strength, Cucker-Smale model, local flocking, mono-cluster flocking, multi-cluster flocking. The work of S.-Y. Ha is supported by the Samsung Science and Technology Foundation under Project Number SSTF-BA1401-03. The work of D. Ko is supported by the fellowship of POSCO TJ Park Foundation. The work of Y. Zhang is partially supported by a National Research Foundation of Korea grant (2014R1A2A2A05002096) funded by the Korean government. ∗ Corresponding author: Yinglong Zhang.
Publisher Copyright:
© 2018 American Institute of Mathematical Sciences. All Rights Reserved.
Keywords
- Critical coupling strength
- Cucker-Smale model
- Local flocking
- Mono-cluster flocking
- Multi-cluster flocking