Relating the Kuramoto model to data from immobile firefly swarms

The Kuramoto Model is arguably the simplest (and, thus, the most tractable) nonlinear model of coupled oscillators. But how well does it represent what is observed in nature? I will present data and analysis from synchronous flashing displays observed in one species of firefly from southeast Asia, that, owing to their relative immobility, offers a unique opportunity for reliable tracking and direct application of candidate models. Our results suggest that firefly interaction is better described by a topological network as opposed to metric-based connectivity usually assumed in models. In addition, on the collective scale, we see meta oscillations of the order parameter over time ("breathing"). We attempt to find the simplest generalization of the Kuramoto model that can reproduce the observed qualitative dynamics; the most parsimonious option incorporates a "phase lag" and nonglobal interactions (dictated by some spatial decay). We thus propose this as a "real world" variant—it captures observed dynamics (and thus informs us about the minimal required ingredients to do so) yet remains tractable. We go one step further and suggest topological instead of metric connectivity; this novel model can also recover the observed breathing, and is also unexplored mathematically.