Abstract
Startle reaction is an alarm behavior observed in animal groups during anti-predatory response or fear-inducing stimulation. This behavior is characterized by spontaneous change in heading direction and increasing speed that can drastically affect group coordination. In this work, we leverage a mathematical model of fish social behavior to recreate startle reaction. Specifically, we model startle reaction through a biased jump diffusion process, where the jumps process captures sudden and fast changes of heading direction observed during this escaping behavior. Then, using extensive numerical simulations, we test their effects on group of fish including an informed individual prescribing the direction of motion and several followers by systematically varying the frequency and intensity of the sudden and fast turns introduced in the heading direction of a single individual. We demonstrate the emergence of novel form of leadership and phase transition between complete ordered states and disorganized states. In addition, we evidence that at specific range of frequencies and amplitudes, the initiation of this behavior might be utilized to divert group followers from their reference trajectory while keeping them in a synchronized state with the startling individual. Our findings offer a new paradigm to recreate the emergence of leadership applicable to divert or contain multi-vehicle systems.
