Cucker-Smale model with normalized communication weights and time delay
By Young-Pil Choi, Jan Haskovec. 2016
117 citations recorded by the source corpus.
We study a Cucker-Smale-type system with time delay in which agents interact with each other through normalized communication weights. We construct a Lyapunov functional for the system and provide sufficient conditions for asymptotic flocking, i.e., convergence to a common velocity vector. We also carry out a rigorous limit passage to the mean-field limit of the particle system as the number of particles tends to infinity.For the resulting Vlasov-type equation we prove the existence, stability and large-time behavior of measure-valued solutions. This is, to our best knowledge, the first such result for a Vlasov-type equation with time delay. We also present numerical simulations of the discrete system with few particles that provide further insights into the flocking and oscillatory behaviors of the particle velocities depending on the size of the time delay.
Subfields: Computer Networks and Communications, Modeling and Simulation, Molecular Biology
View Paper: https://www.semanticscholar.org/paper/f74eaab2e87b2c8c762ba3579844ff37c8dcd046
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In Computer Networks and Communications
In Modeling and Simulation
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Citations in the corpus
- Flocking estimates for the Cucker–Smale model with time lag and hierarchical leadership (2017, background): “Indeed, delayed versions of the standard Cucker-Smale model have been recently considered (see [36, 23, 14, 44]) and flocking results have been proved but only for particular potentials ([36, 14] ) or under appropriate structural assumptions ([23, 44]).”