carolinus fireflies interacting in swarms of increasing density also shows quantitatively similar phenomenology and reduces to the analytic framework in the appropriate limit of the tunable coupling strength. Next, we add further sophistication to the framework using a computational approach featuring groups of random oscillators via integrate-and-fire interactions controlled by a tunable parameter. Remarkably, with no fitting parameters, analytic predictions from this simple principle and framework agree strikingly well with data. Here we propose a mechanism for emergence of synchrony and periodicity, and formulate the principle in a mathematical framework. Yet, when congregating into large mating swarms, these fireflies transition into predictability, synchronizing with their neighbors with a rhythmic periodicity. In isolation from their peers, Photinus carolinus fireflies flash with no intrinsic period between successive bursts.
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