Spontaneous trail formation in populations of auto-chemotactic walkers

Trail formation is known in animal populations. It originates in the traces (pheromones, footsteps, etc.) that individuals leave behind as they move and their response to those left by the others. Such a dynamic landscape, mediated by the traces, results in a delayed and long-range communication between the individuals, and trails may emerge spontaneously from a homogeneous state. We have studied a minimal model consisting of persistent walkers and their chemical secretions. The walkers are modelled as self-propelled particles that deposit and sense the chemicals and act according to an alignment rule: Changing their direction of motion. Based on extensive computer simulations, we identify a number of emerging stationary patterns and obtain qualitatively the non-equilibrium phase diagram of the model. In particular, we show that the model supports the spontaneous formation of persistent macroscopic trails, and we analyse the order parameter of this putative dynamic phase transition. Employing a dynamic model for few macroscopic observables, including the sub-population size of trail-following agents, we gain insight into the early phase of trail formation.

Z. Mokhtari, R. I. A. Patterson, and F. Höfling, ZIB Report 21-36 (2021), urn:nbn:de:0297-zib-84466, submitted to New. J. Phys.

Link: https://nbn-resolving.org/urn:nbn:de:0297-zib-84466