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

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.