Co-evolving agents subject to local versus nonlocal barycentric interactions

TL;DR

This paper analyzes the mean-field dynamics of stochastic agents with local and nonlocal barycentric interactions, revealing a transition from diffusion to flocking behavior depending on interaction range.

Contribution

It introduces an analytically solvable model for agent interactions with barycentric modulation, highlighting the transition between diffusive and flocking regimes.

Findings

Transition from diffusive to flocking behavior

Flocking characterized by solitary wave solutions

Analytical solution of a two-velocity Boltzmann model

Abstract

The mean-field dynamics of a collection of stochastic agents with local versus nonlocal interactions is studied via analytically soluble models. The nonlocal interactions result from a barycentric modulation of the observation range of the agents. Our modeling framework is based on a discrete two-velocity Boltzmann dynamics which can be analytically discussed. Depending on the span and the modulation of the interaction range, we analytically observe a transition from a purely diffusive regime without definite pattern to a flocking evolution represented by a solitary wave traveling with constant velocity.