Mechanism underlying the diverse collective behavior in the swarm oscillator model

The swarm oscillator model describes the long-time behavior of interacting chemotactic particles, and it shows numerous types of macroscopic patterns. However, the reason why so many kinds of patterns emerge is not clear. In this study, we elucidate the mechanism underlying the diversity of the pattens by analyzing the model for two particles. Focusing on the behavior when the two particles are spatially close, we find that the dynamics is classified into eight types, which explain most of the observed 13 types of patterns.