Startle Response Triggers Collective Phase Transitions in Schooling Fish*

Schooling fish often self-organize into collective patterns such as swarming, milling, or polarized schooling. A group of fish can transition between distinct states due to changes in behavioral rules, environmental factors, or stochastic events. A common stochastic event in fish schools is the startle response to perceived risk; startle is a socially contagious behavior that can propagate through the group, regardless of the presence of an external stimulus. Here, using known self-propelled particle models, we explore how individual-level startle responses influence the switch between distinct group motions in fish schools. This work contributes to understanding the mechanisms behind dynamic transitions and the propagation of responses to risk in collective animal behavior.