Coordination is ubiquitous in living systems. Existing theoretical models of coordination — from bacteria to brains — focus on either gross statistics in large-scale systems (N→∞) or detailed dynamics in small-scale systems (mostly N=2). Both approaches have proceeded largely independent of each other. The present work bridges this gap with a theoretical model of biological coordination that captures key experimental observations of mid-scale social coordination at multiple levels of description. It also reconciles in a single formulation two well-studied models of large- and small-scale biological coordination (Kuramoto and extended Haken-Kelso-Bunz). The model adds second-order coupling (from extended Haken-Kelso-Bunz) to the Kuramoto model. We show that second-order coupling is indispensable for reproducing empirically observed phenomena and gives rise to a phase transition from mono- to multi-stable coordination across scales. This mono-to-multistable transition connects the emergence and growth of behavioral complexity in small and large systems.
Connecting empirical phenomena and theoretical models of biological coordination across scales
Mengsen Zhang, Christopher Beetle, J. A. Scott Kelso, Emmanuelle Tognoli