Analysis of a model of self-propelled agents interacting through pheromone

Abstract

Abstract We establish well-posedness for a model of self-propelled agents interacting through pheromone which they themselves produce. The model consists of an arbitrary number of agents modeled by a system of ordinary differential equations, for which the acceleration term includes the influence of a chemical signal, or pheromone, which induces a turning-like behaviour. The signal is produced by the agents themselves and obeys a diffusion equation. We prove that the resulting system, which is non-local in both time and space, enjoys well-posedness properties, using a fixed point method, and show some numerical results.