This paper presents a review and critical analysis on the modeling of the dynamics of
vehicular traffic, human crowds and swarms seen as living and, hence, complex systems. It …

A review of the mean field limits for Vlasov equations AIMS share this content in Facebook
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Synchronization occurs in many natural and technological systems, from cardiac pacemaker
cells to coupled lasers. In the synchronized state, the individual cells or lasers coordinate the …

The description of emerging collective phenomena and self-organization in systems
composed of large numbers of individuals has gained increasing interest from various …

We present a comprehensive study of Vicsek-style self-propelled particle models in two and
three space dimensions. The onset of collective motion in such stochastic models with only …

In this paper, we analyze the asymptotic behavior of solutions of the continuous kinetic
version of flocking by Cucker and Smale [IEEE Trans. Automat. Control, 52 (2007), pp. 852 …

We review the state-of-the-art in the modelling of the aggregation and collective behavior of
interacting agents of similar size and body type, typically called swarming. Starting with …

We describe a setting where convergence to consensus in a population of autonomous
agents can be formally addressed and prove some general results establishing conditions …

We review some classical and more recent results for the derivation of mean field equations
from systems of many particles, focusing on the stochastic case where a large system of …

These notes are devoted to a summary on the mean-field limit of large ensembles of
interacting particles with applications in swarming models. We first make a summary of the …