Emergent behavioural phenotypes of swarming models revealed by mimicking a frustrated anti-ferromagnet.

D J G Pearce,M S Turner

doi:10.1098/rsif.2015.0520

Abstract

Self-propelled particle (SPP) models are often compared with animal swarms. However, the collective animal behaviour observed in experiments often leaves considerable unconstrained freedom in the structure of a proposed model. Essentially, multiple models can describe the observed behaviour of animal swarms in simple environments. To tackle this degeneracy, we study swarms of SPPs in non-trivial environments as a new approach to distinguish between candidate models. We restrict swarms of SPPs to circular (periodic) channels where they polarize in one of two directions (like spins) and permit information to pass through windows between neighbouring channels. Co-alignment between particles then couples the channels (anti-ferromagnetically) so that they tend to counter-rotate. We study channels arranged to mimic a geometrically frustrated anti-ferromagnet and show how the effects of this frustration allow us to better distinguish between SPP models. Similar experiments could therefore improve our understanding of collective motion in animals. Finally, we discuss how the spin analogy can be exploited to construct universal logic gates, and therefore swarming systems that can function as Turing machines.

Highlights

Collective motion in large groups of animals represents one of the most conspicuous displays of emergent order in nature [1,2,3,4]
For weak interactions, little difference is observed in the behaviour of the swarms, both having a polarized state which rarely changes direction (figure 2)
Self-propelled particle (SPP) with metric-free interactions exhibit high polarization and long polarization autocorrelation times, tPz: As these swarms clump into bands, the majority of nearest neighbours remain sited in the same channel, which leads to a weaker coupling between swarms in adjacent channels; this allows them to pass each other without a significant effect on the polarization

Summary

Introduction

Collective motion in large groups of animals represents one of the most conspicuous displays of emergent order in nature [1,2,3,4]. By observing swarms of a limited size, it is possible to see what reaction an individual has to its immediate neighbours and infer a set of rules that give rise to the observed behaviour [21 –23] While informative, this approach still leaves structural freedom in how one constructs a model to give rise to the observed behaviour. Another method is to take a maximum entropy approach [24 –26], finding the model with the minimum structure that is consistent with observations This technique has been used to show that pairwise interactions are sufficient to explain order propagation through the entirety of a flock of starlings and support the conclusion that interactions governing starling flocks are topological in nature [24]. The essential difficulty of model building still remains: it is an inverse problem in which no complete set of techniques yet exist to perform this inversion

Methods

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Discussion

Conclusion