Abstract
We propose a simple adaptive-network model describing recent swarming experiments. Exploiting an analogy with human decision making, we capture the dynamics of the model using a low-dimensional system of equations permitting analytical investigation. We find that the model reproduces several characteristic features of swarms, including spontaneous symmetry breaking, noise- and density-driven order–disorder transitions that can be of first or second order, and intermittency. Reproducing these experimental observations using a non-spatial model suggests that spatial geometry may have less of an impact on collective motion than previously thought.
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GENERAL SCIENTIFIC SUMMARY Introduction and background. To understand how groups of self-propelled individuals (such as bird flocks, fish schools or insect swarms) make collective decisions, simple, low-dimensional descriptions of population-level behaviour are highly desirable. In closely related research on human decision making, analytically tractable modelling approaches based on network theory are used.
Main results. We introduce a simple adaptive-network model describing swarming experiments by Buhl et al (2006 Science 312 1402–6), where groups of locusts march freely in a ring-shaped arena. At low insect densities, no ordered collective motion is observed, whereas at high insect densities a common persistent marching direction emerges. Our model captures these two regimes and identifies the swarming transition as a (subcritical or supercritical) pitchfork bifurcation. It also reproduces an intermittent switching of direction displaying memory effects. These results are obtained analytically and numerically and do not require an underlying geometrical space.
Wider implications. By likening swarming to opinion formation in humans, we connected two areas of research usually considered separately. Our analysis unveils the essential elements required to reproduce the observed collective behaviour. Given the generality of the model, we expect it to be applicable to a large class of systems.