# A particle system approach to aggregation phenomena

## TL;DR

This paper introduces a particle system model for aggregation phenomena, demonstrating that the empirical density converges to a PDE-ODE system solution, bridging individual interactions with macroscopic behavior.

## Contribution

It presents a novel particle system approach that rigorously links individual-based models to PDE-ODE descriptions of aggregation.

## Key findings

- Empirical density converges to PDE-ODE solution.
- Provides mathematical proof of convergence.
- Connects microscopic interactions with macroscopic aggregation patterns.

## Abstract

Inspired by a PDE-ODE system of aggregation developed in the biomathematical literature, an interacting particle system representing aggregation at the level of individuals is investigated. It is proved that the empirical density of the individual converges to solution of the PDE-ODE system.