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Coordination is ubiquitous in living systems. Existing theoretical models ofcoordination -- from bacteria to brains -- focus on either gross statistics inlarge-scale systems ($N\rightarrow\infty$) or detailed dynamics in small-scalesystems (mostly $N=2$). Both approaches have proceeded largely independent ofeach other. The present work bridges this gap with a theoretical model ofbiological coordination that captures key experimental observations ofmid-scale social coordination at multiple levels of description. It alsoreconciles in a single formulation two well-studied models of large- andsmall-scale biological coordination (Kuramoto and extended Haken-Kelso-Bunz).The model adds second-order coupling (from extended Haken-Kelso-Bunz) to theKuramoto model. We show that second-order coupling is indispensable forreproducing empirically observed phenomena and gives rise to a phase transitionfrom mono- to multi-stable coordination across scales. This mono-to-multistabletransition connects the emergence and growth of behavioral complexity in smalland large systems.

Connecting empirical phenomena and theoretical models of biological coordination across scales