3 years ago

Particle Interactions Mediated by Dynamical Networks: Assessment of Macroscopic Descriptions

D. Peurichard, J. Barré, J. A. Carrillo, E. Zatorska, P. Degond

Abstract

We provide a numerical study of the macroscopic model of Barré et al. (Multiscale Model Simul, 2017, to appear) derived from an agent-based model for a system of particles interacting through a dynamical network of links. Assuming that the network remodeling process is very fast, the macroscopic model takes the form of a single aggregation–diffusion equation for the density of particles. The theoretical study of the macroscopic model gives precise criteria for the phase transitions of the steady states, and in the one-dimensional case, we show numerically that the stationary solutions of the microscopic model undergo the same phase transitions and bifurcation types as the macroscopic model. In the two-dimensional case, we show that the numerical simulations of the macroscopic model are in excellent agreement with the predicted theoretical values. This study provides a partial validation of the formal derivation of the macroscopic model from a microscopic formulation and shows that the former is a consistent approximation of an underlying particle dynamics, making it a powerful tool for the modeling of dynamical networks at a large scale.

Publisher URL: https://link.springer.com/article/10.1007/s00332-017-9408-z

DOI: 10.1007/s00332-017-9408-z

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