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While mathematical models, in particular self-propelled particle (SPP)models, capture many of the observed properties of large fish schools, they donot always capture the interactions of smaller shoals. Nor do these models tendto account for the observation that, when swimming alone or in smaller groups,many species of fish use intermittent locomotion, often referred to as burstand coast or burst and glide. Recent empirical studies have suggested thatburst and glide movement is indeed pivotal to the social interactions ofindividual fish. In this paper, we propose a model of social burst and glidemotion by combining a well-studied model of neuronal dynamics, theFitzHugh-Nagumo model, with a model of fish motion. We begin by showing thatthe model can capture the motion of a single fish swimming down a channel. Bythen extending to a two fish model, where visual stimuli of the position of theother fish affect the internal burst or glide state of the fish, we find thatour model captures a rich set of swimming dynamics found in many species offish. These include: leader-follower behaviour; periodic changes in leadership;apparently random (i.e. chaotic) leadership change; and pendulum-liketit-for-tat turn taking. Unlike SPP models, which assume that fish move at aconstant speed, the model produces realistic motion of individual fish.Moreover, unlike previous studies where a random component is used forleadership switching to occur, we show that leadership switching, both periodicand chaotic, can be the result of a deterministic interaction. We give severalempirically testable predictions on how fish interact and discuss our resultsin light of recently established correlations between fish locomotion and brainactivity.

Using neuronal models to capture burst and glide motion and leadership in fish