Asymmetric Interactions Induce Bistability and Switching Behavior in Models of Collective Motion

Moving animal groups often spontaneously change their group structure and dynamics, but standard models used to explain collective motion in animal groups are typically unable to generate changes of this type. Recently, a model based on attraction, repulsion and asymmetric interactions designed for specific fish experiments was shown capable of producing such changes. However, the origin of the model’s ability to generate them, and the range of this capacity, remains unknown. Here we modify and extend this model to address these questions. We establish that its ability to generate groups exhibiting changes depends on the size of the blind zone parameter $\beta$. Specifically, we show that for small $\beta$ swarms and mills are generated, for larger $\beta$ polarized groups forms, and for a region of intermediate $\beta$ values there is a bistability region where continuous switching between milling and polarized groups occurs. We also show that the location of the bistability region depends on group size and the relative strength of velocity alignment when this interaction is added to the model. These findings may contribute to advance the use of self-propelled particle models to explain a range of disruptive phenomena previously thought to be beyond the capabilities of such models.