Agent-Based Simulation of the Two-Dimensional Patlak-Keller-Segel Model

TL;DR

This paper introduces an agent-based simulation method for the 2D Patlak-Keller-Segel model, effectively capturing chemotactic aggregation and threshold phenomena with results aligning with analytical predictions.

Contribution

It presents a novel particle-based simulation approach to model chemotactic interactions and singular aggregation in the Patlak-Keller-Segel equation.

Findings

Simulation results match analytical threshold predictions

Effective modeling of singular aggregation phenomena

Agent-based approach captures chemotactic dynamics

Abstract

The Patlak-Keller-Segel equation describes the chemotactic interactions of small organisms in the continuum limit, and a singular peak appears through spontaneous aggregation when the total mass of the organisms exceeds a critical value. To deal with this singular behavior numerically, we propose an agent-based simulation method in which both the organisms and the chemicals are represented as particles. Our numerical estimates for the threshold behavior are consistent with the analytic predictions.