Kinetic Limits for Pair-Interaction Driven Master Equations and Biological Swarm Models
Artikel i vetenskaplig tidskrift, 2013

We consider a class of stochastic processes modeling binary interactions in an N-particle system. Examples of such systems can be found in the modeling of biological swarms. They lead to the definition of a class of master equations that we call pair-interaction driven master equations. In the spatially homogeneous case, we prove a propagation of chaos result for this class of master equations which generalizes Mark Kac's well-known result for the Kac model in kinetic theory. We use this result to study kinetic limits for two biological swarm models. We show that propagation of chaos may be lost at large times and we exhibit an example where the invariant density is not chaotic.

spectral

kinetic equations

propagation of chaos

behavior

continuum-limit

boltzmann-equation

stochastic particle approximations

gap

limit

Kac's master

vacuum

binary interactions

system

global validity

3-dimensional rare-gas

mean-field

Master equation

Författare

E. Carlen

Rutgers, The State University of New Jersey

P. Degond

CNRS Centre National de la Recherche Scientifique

Université de Toulouse

Bernt Wennberg

Göteborgs universitet

Chalmers, Matematiska vetenskaper, Matematik

Mathematical Models and Methods in Applied Sciences

0218-2025 (ISSN)

Vol. 23 1339-1376

Ämneskategorier

Matematik

Fundament

Grundläggande vetenskaper

DOI

10.1142/S0218202513500115