Unifying Large- and Small-Scale Theories of Coordination

Abstract

Coordination is a ubiquitous feature of all living things. It occurs by virtue of informational coupling among component parts and processes and can be quite specific (as when cells in the brain resonate to signals in the environment) or nonspecific (as when simple diffusion creates a source–sink dynamic for gene networks). Existing theoretical models of coordination—from bacteria to brains to social groups—typically focus on systems with very large numbers of elements (N→∞) or systems with only a few elements coupled together (typically N = 2). Though sharing a common inspiration in Nature’s propensity to generate dynamic patterns, both approaches have proceeded largely independent of each other. Ideally, one would like a theory that applies to phenomena observed on all scales. Recent experimental research by Mengsen Zhang and colleagues on intermediate-sized ensembles (in between the few and the many) proves to be the key to uniting large- and small-scale theories of coordination. Disorder–order transitions, multistability, order–order phase transitions, and especially metastability are shown to figure prominently on multiple levels of description, suggestive of a basic Coordination Dynamics that operates on all scales. This unified coordination dynamics turns out to be a marriage of two well-known models of large- and small-scale coordination: the former based on statistical mechanics (Kuramoto) and the latter based on the concepts of Synergetics and nonlinear dynamics (extended Haken–Kelso–Bunz or HKB). We show that models of the many and the few, previously quite unconnected, are thereby unified in a single formulation. The research has led to novel topological methods to handle the higher-dimensional dynamics of coordination in complex systems and has implications not only for understanding coordination but also for the design of (biorhythm inspired) computers.

Collective dynamics support group drumming, reduce variability, and stabilize tempo drift

“…We showed that this result agrees with a collective dynamics framework based on an adapted Kuramoto model. The model is consistent with the idea from theoretical biology that self-organizing systems can successfully coordinate with an external constraint by reducing their disorder at the macro-level at the expense of increasing their micro-level disorder (Kugler & Turvey, 1987;Prokopenko, Polani, & Ay, 2014) and that medium-sized groups exhibit commonalities with principles of organization found both in two-unit and large collectives (Kelso, 2021;Zhang et al, 2019). Interestingly, in the octet group, individual variability was similar in both the synchronization-only condition, where the metronome pacing stimulus was present, and in the self-paced continuation stage of the SCT trials, where no pacing stimulus was present.…”

“…In short, the one approach posits prediction for synchronization, the other, synchronization for prediction. An important benefit of the latter is that it naturally scales up to explain coordination in larger groups, converging on the same formalisms used for collective behaviour in animals (Kelso, 2021;Zhang, Beetle, Kelso, & Tognoli, 2019). Here we consider such a system of coupled oscillators to account for variability in a group of drumming individuals.…”

multiSyncPy: A Python Package for Assessing Multivariate Coordination Dynamics

“…Our methods are also appropriate in situations where there are numerous variables and it would be difficult to make sense of a large number of pairwise synchronizations. In other words, we aim to contribute tools that may advance the fields understanding of how coordination functions across scales (Kelso, 2021;Zhang et al, 2019). For the benefit of future researchers interested in multivariate coordination dynamics, multiSyncPy is made freely available under the liberal…”

The Haken–Kelso–Bunz (HKB) model: from matter to movement to mind

“…The latter turns out to be a marriage of Kuramoto and HKB models (Zhang et al 2019; see "Appendix" for a summary of the mathematical models). This Generalized HKB model (Kelso 2021) handles how a diverse group of complex (human) agents interact with each other when their actions influence-and are influenced by-the rest of the ensemble in unpredictable ways, and appears to be a key step toward embracing coordinative complexity. By going beyond synchrony, per se it promises a deeper understanding of collective behavior in all kinds of settings, from groups of neurons to groups of animals and people (e.g., Bardy et al 2020;Couzin 2018).…”