EF4 – Particles and Agents



Coherent Movements in Co-evolving Agent–Message Systems

Project Heads

Felix Höfling, Robert I.A. Patterson

Project Members

Zahra Mokhtari

Project Duration

First funding period: 01.01.2021 − 31.12.2021; Second funding period: 01.01.2022 − 31.12.2023

Located at

FU Berlin


The dynamics of social systems emerges from the behaviour and interaction of individual agents. A key question in the field is which basic rules and mechanisms can generate a certain observed phenomenon on the population scale? For example, in the context of opinion dynamics classical voter models show that neighbour contacts can lead to clustering, termed as opinion alignment. However often, the direct exchange of opinions between individuals is an idealisation, opinions are typically not black or white, and they change rarely by a single event (e.g., an election campaign). Instead, opinions form gradually by consuming a large number of small messages such as direct chats with peers, but nowadays with increasing importance also due to short texts (tweets, whatsapp, news) focussed on few specific topics.
In particular, each message has the potential to influence many individuals over an extended period of time.
Such a message passing requires coupling the agent dynamics to a co-evolving secondary field encoding the messages. Specifically, agents leave many small and volatile messages behind that can influence other agents until they disappear. Here, we aim to investigate the formation and fragmentation of opinions under a message-based communication. Our ultimate goal is to understand what makes a group of people sharing similar opinions change their opinion coherently under otherwise unchanged external conditions?
Animal systems and cell cultures exhibit a closely related message-based interaction known as auto-chemotaxis. There, the agents move in real space and preferentially towards high concentrations of a pheromone (a signalling chemical) that they produce themselves. This leads to a delayed and long-range coupling between agents and intriguing collective behaviour, such as trail formation. Continuum mathematical models of auto-chemotaxis are traditionally based on the Patlak–Keller–Segel equations (PKS), a system of two partial differential equations for the density of agents and 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 introduce an agent-based model for self-propelled particles that make oriented deposits of pheromones and also sense such deposits to which they then respond with gradual changes of their direction of motion. Based on extensive off-lattice computer simulations aiming at the scale of insects, e.g. ants, we identify a number of emerging stationary patterns and obtain qualitatively the non-equilibrium state diagram of the model, spanned by the strength of the agent–pheromone interaction and the number density of the population. In particular, we demonstrate the spontaneous formation of persistent, macroscopic trails, and highlight some behaviour that is consistent with a dynamic phase transition. This includes a characterisation of the mass of system-spanning trails as a potential order parameter. We also propose a dynamic model for a few macroscopic observables, including the sub-population size of trail-following agents, which captures the early phase of trail formation.

External Website

Related Publications

Mokhtari Z, Patterson RI, Höfling F. Spontaneous trail formation in populations of auto-chemotactic walkers. New Journal of Physics. 2022 Jan 5;24(1):013012.
Irani E, Mokhtari Z, Zippelius A. Dynamics of bacteria scanning a porous environment. Physical Review Letters. 2022 Apr 5;128(14):144501.

Related Pictures

The aligning interaction between agents (close-up: disks) and their deposited pheromones (dots) gives rise to macroscopic structures such as system-spanning trails and rotating clusters.
Representative configurations of agent positions for different values of crowdedness and the relative alignment strengths.