<p>Collective motion is a phenomenon observed in many animal species, and is characterized by the emergence of ordered motion in groups where individuals only perceive their immediate neighbours. Vortex formation (milling) is a natural phenomenon of particular interest in fish; however, the cause and dynamics of milling are not well understood. In this paper, we use a minimal swarming model that incorporates individual agent behaviour and we perform computational simulations to investigate mills formed in two dimensions. We explain complex mill dynamics in terms of neighbour-induced individual behaviour. We show that feasible mill geometry is limited by individual’s swim speed and maximal turning rate. We find that mill oscillation is an induced property of emergent mills and results from individuals following fixed circular paths. With these results, we perform a mill stability regime analysis. We show that stable mills form when individual behaviour comes into balance with the distribution of neighbours. This lays the foundation for a statistically predictive view of mill formation. By considering the effect of individuals on the swarm, rather than just of the swarm on the individual, we advance the understanding of mill dynamics and help to illuminate why mills form and persist and under what conditions.</p>

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Effects of induced behaviour on vortex formation and stability in swarms

  • Flora Grilli,
  • Grgur Tokić,
  • Dick K. P. Yue

摘要

Collective motion is a phenomenon observed in many animal species, and is characterized by the emergence of ordered motion in groups where individuals only perceive their immediate neighbours. Vortex formation (milling) is a natural phenomenon of particular interest in fish; however, the cause and dynamics of milling are not well understood. In this paper, we use a minimal swarming model that incorporates individual agent behaviour and we perform computational simulations to investigate mills formed in two dimensions. We explain complex mill dynamics in terms of neighbour-induced individual behaviour. We show that feasible mill geometry is limited by individual’s swim speed and maximal turning rate. We find that mill oscillation is an induced property of emergent mills and results from individuals following fixed circular paths. With these results, we perform a mill stability regime analysis. We show that stable mills form when individual behaviour comes into balance with the distribution of neighbours. This lays the foundation for a statistically predictive view of mill formation. By considering the effect of individuals on the swarm, rather than just of the swarm on the individual, we advance the understanding of mill dynamics and help to illuminate why mills form and persist and under what conditions.