Emergent behavior of Cucker-Smale model with normalized weights and distributed time delays
Young-Pil Choi, Cristina Pignotti · Networks and Heterogeneous Media · 2019
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.