Existence and approximation of probability measure solutions to models of collective behaviors

TL;DR

This paper develops an existence and approximation framework for models of collective behavior based on probability measures, applicable to crowd and swarm dynamics, using mass conservation equations.

Contribution

It introduces a new theoretical approach for analyzing solutions to collective behavior models formulated with probability measures.

Findings

Established existence of solutions for the models

Provided approximation methods for these solutions

Validated the framework with crowd and swarm models

Abstract

In this paper we consider first order differential models of collective behaviors of groups of agents based on the mass conservation equation. Models are formulated taking the spatial distribution of the agents as the main unknown, expressed in terms of a probability measure evolving in time. We develop an existence and approximation theory of the solutions to such models and we show that some recently proposed models of crowd and swarm dynamics fit our theoretic paradigm.