Two-network Kuramoto-Sakaguchi model under tempered stable Lévy noise

Calibrating coupling for collaboration with Kuramoto

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, normalizing 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 synchronization 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 organization. Our results suggest larger maximum team sizes than early management science proposes, but are consistent with studies that focus only the relationship between supervisor and subordinates, excluding other internal interactions in the team.

Emergent behavior in an adversarial synchronization and swarming model

We consider a red-versus-blue coupled synchronization and spatial swarming (i.e., swarmalator) model that incorporates attraction and repulsion terms and an adversarial game of phases. The model exhibits behaviors such as spontaneous emergence of tactical manoeuvres of envelopment (e.g., flanking, pincer, and envelopment) that are often proposed in military theory or observed in nature. We classify these states based on a large set of features such as spatial densities, synchronization between clusters, and measures of cluster distances. These features are used to study the influence of coupling parameters on the expected presence of these states and the-sometimes sharp-transitions between them.