Continuum limit of self-driven particles with orientation interaction

By Pierre Degond, Sébastien Motsch. 2007

357 citations recorded by the source corpus.

The discrete Couzin–Vicsek algorithm (CVA), which describes the interactions of individuals among animal societies such as fish schools is considered. In this paper, a kinetic (mean-field) version of the CVA model is proposed and its formal macroscopic limit is provided. The final macroscopic model involves a conservation equation for the density of the individuals and a non-conservative equation for the director of the mean velocity and is proved to be hyperbolic. The derivation is based on the introduction of a non-conventional concept of a collisional invariant of a collision operator.

Subfields: Applied Mathematics, Computer Networks and Communications, Modeling and Simulation

View Paper: https://www.semanticscholar.org/paper/1d368675fca1c887ca448d19d4c6ec3ab107df76

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In Applied Mathematics

In Computer Networks and Communications

In Modeling and Simulation

Citations in the corpus

A simple proof of the Cucker-Smale flocking dynamics and mean-field limit (2009, methodology): “We refer to Degond and Motsch’s works [4, 5, 6 ] for recent kinetic description of Viscek type model for ocking.”
On the Modeling of Traffic and Crowds: A Survey of Models, Speculations, and Perspectives (2011, background): “Moreover, although the scaling and representation are analogous, different modeling approaches have been proposed, such as stochastic differential equations [1], macroscopic equations derived from stochastic perturbation of individual dynamics [41], [63], modeling swarming patterns [25], [201], and ”
A Kinetic Flocking Model with Diffusion (2010, background): “1 Main results Description of the collective and interactive motion of multi-agents such as school of fish, flocking of birds or swarm of bacteria became recently a major research topic in population and behavioral biology and ecology [23, 4, 19, 20, 5, 6].”
Flocking estimates for the Cucker–Smale model with time lag and hierarchical leadership (2017, background): “[15, 17, 27, 37, 40, 46, 50, 52]), stochastic terms ([18, 23, 25]), pedestrian crowds (see [16, 31]), infinite-dimensional kinetic models (see [1, 4, 9, 12, 22, 28, 49]), topological models ([5, 29]), control models (see [6, 10, 11, 43, 51]).”
Asymptotic Flocking Dynamics for the Kinetic Cucker-Smale Model (2010, background): “In the biological context, the emergent behavior of bird flocks, fish schools, or bacteria aggregations, among others, is a major research topic in population and behavioral biology and ecology [1, 4, 14, 15, 16, 18, 30, 33, 34].”
Double milling in self-propelled swarms from kinetic theory (2009, background): “While several continuum models based on heuristic derivations have been presented in the literature, few attempts have been made at deriving such models starting from principles of dynamics of individual agents [5, 9, 20, 13, 14].”
Large Scale Dynamics of the Persistent Turning Walker Model of Fish Behavior (2007, neutral): “AMS Subject classification: 35Q80, 35K99, 60J70, 82C31, 82C41, 82C70, 82C80, 92D50 1”
A New Model for Self-organized Dynamics and Its Flocking Behavior (2011, background): “2), we can derive the macroscopic limit of the dynamics [10, 11, 15].”
On collision-avoiding initial configurations to Cucker-Smale type flocking models (2012, background): “Introduction Flocking phenomena [3, 11, 12, 13, 14, 32, 33, 34] such as flocking of birds, schooling of fishes, and swarming of bacteria are often observed in complex biological systems, and are some of the collective self-organizing phenomena in biological, mechanical, and social groups of self-pro”