We study a Cucker-Smale-type flocking model with distributed time delay where individuals interact with each other through normalized communication weights. Based on a Lyapunov functional approach, we provide sufficient conditions for the velocity alignment behavior. We then show that as the number of individuals N tends to infinity, the N-particle system can be well approximated by a delayed Vlasov alignment equation. Furthermore, we also establish the global existence of measure-valued solutions for the delayed Vlasov alignment equation and its large-time asymptotic behavior.
|Number of pages||16|
|Journal||Networks and Heterogeneous Media|
|Publication status||Published - 2019 Dec 1|
Bibliographical noteFunding Information:
2010 Mathematics Subject Classification. Primary: 34A12, 34D05; Secondary: 35Q83. Key words and phrases. Cucker-Smale model, time delay, flocking, Vlasov equation. The first author was supported by National Research Foundation of Korea(NRF) grant funded by the Korea government(MSIP) (No. 2017R1C1B2012918 and 2017R1A4A1014735) and POSCO Science Fellowship of POSCO TJ Park Foundation. The research of the second author was partially supported by the GNAMPA 2018 project Analisi e controllo di modelli differenziali non lineari (INdAM) . ∗ Corresponding author: Cristina Pignotti.
© American Institute of Mathematical Sciences.
All Science Journal Classification (ASJC) codes
- Statistics and Probability
- Computer Science Applications
- Applied Mathematics