Kinetic theory of particle interactions mediated by dynamical networks
Abstract
We provide a detailed multiscale analysis of a system of particles interacting through a dynamical network of links. Starting from a microscopic model, via the mean field limit, we formally derive coupled kinetic equations for the particle and link densities, following the approach of [Degond et al., M3AS, 2016]. Assuming that the process of remodelling the network is very fast, we simplify the description to a macroscopic model taking the form of single aggregation-diffusion equation for the density of particles. We analyze qualitatively this equation, addressing the stability of a homogeneous distribution of particles for a general potential. For the Hookean potential we obtain a precise condition for the phase transition, and, using the central manifold reduction, we characterize the type of bifurcation at the instability onset.
Keywords
Cite
@article{arxiv.1607.01975,
title = {Kinetic theory of particle interactions mediated by dynamical networks},
author = {Julien Barré and Pierre Degond and Ewelina Zatorska},
journal= {arXiv preprint arXiv:1607.01975},
year = {2016}
}
Comments
33 pages, 5 figures