Department of Mathematics

Collective Motion from Local Attraction

What local interaction rules are used by the individuals in a school of fish or a flock of birds? Since the mid 90's a large number of so called self-propelled particle (spp) models have been introduced and studied to address this question, but at present there are definitely pieces missing. Most of these models include some mix of the three fundamental interactions: attraction, repulsion and orientation. Local attraction alone had not been investigated before [1] and it turned out to be surprisingly rich. In particular, it produces groups exhibiting collective motion with nontrivial internal dynamics and do in fact induce an orientation effect when the standard blind angle is introduced. The aim of this project is to investigate the role and potential of local attraction in models of collective motion in 2 and 3 dimensions. What kind of groups can it produce? What are their stability properties? Hysteresis? How is the effect of local attraction affected by the introduction of repulsion and orientation? To what extent is local attraction a driving force in real flocks/schools?