Modeling and Analysis of Synchronous Behavior in Biological Systems

Abstract: How does collective synchronous behavior emerge in living systems? We focus on two readily observable and malleable systems: firefly swarms (flashing in unison) and groups of fiddler crabs (waving their large claws in sync). In both examples, these groups are composed of males attempting to woo females through such collective displays. Our research will use four complementary approaches: (i) fieldwork to compile unparalleled new datasets (including the development and employment of novel experimental paradigms, perturbing animals with artificial conspecifics in the wild), (ii) development of new mathematical models for understanding the mechanism underlying biological sync (with potential implications for broader evolutionary theory), (iii) monitoring of a firefly population for conservational efforts, and (iiii) outreach and dissemination of our models and results to the public via podcast, visual arts, and print journalism. On the mathematical side, we are particularly interested in novel coupled oscillator models that can exhibit both phase synchrony and “breathing” chimera states that have been glimpsed in preliminary data. These models include oscillators coupled not just through phase but also through amplitude and / or frequency. We will explore such models on coupling networks of increasing realism, and we also plan to study the model selection problem in the context of oversampled dynamical data, where conventional approaches may need to be modified.