Calibrating Coupling for Collaboration with Kuramoto

Abstract

We calibrate a Kuramoto model inspired representation of peer-to-peer collaboration using data on the maximum team-size where coordination breaks down. The Kuramoto model is modified, normalising the coupling by the degree of input and output nodes, reflecting dispersion of cognitive resources in both absorbing incoming-and tracking outgoing-information. We find a critical point, with loss of synchronisation as the number of nodes grows and analytically determine this point and calibrate the coupling with the known maximum team size. We test that against the known `span of control' for a leader/supervisor organisation. Our results suggest larger maximum team sizes than early management science proposes, but are consistent with recent studies.