EF4 – Particles and Agents



Trail Formation in Populations of Auto-Chemotactic Agents

Project Heads

Felix Höfling, Robert I.A. Patterson

Project Members

Zahra Mokhtari

Project Duration

01.01.2021 − 31.12.2021

Located at

FU Berlin


In auto-chemotaxis agents (cells, organisms, …) move towards high concentrations of a pheromone (signalling chemical) that they produce themselves. This leads to a delayed and long-range coupling between agents and intriguing collective phenomena, such as trail formation and colonisation by ants and the foraging strategies of micro-organisms.

Continuum mathematical models of auto-chemotaxis are traditionally based on the Patlak– Keller–Segel equations (PKS), a system of two partial differential equations: one for the density of agents and one for the concentration of a pheromone.  This is a very reasonable phenomenological model, but it offers little insight into how agents (e.g. ants) might take decisions.

We plan to clarify the kind of cooperative behaviours that enable large populations of agents to establish and follow trails for long distances by studying hydrodynamic limits of agent-based models using hybrid simulations and stochastic process convergence theory.

Diagonal trails wrapping round a square

Spontaneously formed trails. Raw simulation results (left), after image processing (right).

The figure shows the trails spontaneously formed by a minimal agent-based model starting from an homogeneous state. We identify the trails as percolating objects through the system, utilizing image processing techniques.

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