CIM Seminar with Linnéa Gyllingberg

Abstract: While mathematical models, in particular self-propelled particle (SPP) models, capture many of the observed properties of large fish schools, they do not always capture the interactions of smaller shoals. Nor do these models tend to account for the observation that, when swimming alone or in smaller groups, many species of fish use intermittent locomotion, often referred to as burst and coast or burst and glide. In this talk we present a model of social burst and glide motion by combining a well-studied model of neuronal dynamics, the FitzHugh-Nagumo model, with a model of fish motion. Our model captures a rich set of swimming dynamics found in many species of fish. These include: leader-follower behaviour; periodic changes in leadership; apparently random (i.e. chaotic) leadership change; and pendulum-like tit-for-tat turn taking. Unlike SPP models, which assume that fish move at a constant speed, the model produces realistic motion of individual fish. Moreover, unlike previous studies where a random component is used for leadership switching to occur, we show that leadership switching, both periodic and chaotic, can be the result of a deterministic interaction.

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