Elasticity- and consensus-based mechanisms for self-organization in active systems

Self-organization is often observed in active systems such as cell colonies, developing tissue, insect swarms, bird flocks, and groups of autonomous robots. In recent years, several minimal models have been introduced to understand the underlying mechanisms that can lead to the emergence of collective coordinated motion in such systems for different types of individual interactions.

In this work, we consider models with two distinct classes of interactions. In the first class, where interactions are based on relative headings, collective motion results from a standard decentralized consensus process that resembles ferromagnetic ordering and is driven by local alignment forces. In the second class, where they are based on relative positions, self-organization emerges from a novel elasticity-driven process resulting from local attraction-repulsion forces. Using simulations and analytical calculations, we show that these different interactions lead to distinct self-organizing mechanisms and characterize their properties. By developing a formalism based on elastic modes, we show that both mechanisms follow different principles and can reach different self-organized states.