Beyond in-phase and anti-phase coordination in a model of joint action

TL;DR

This paper explores the full dynamics of the HKB model of joint action, revealing new coordination regimes and stability boundaries through detailed bifurcation analysis, extending understanding beyond traditional approximations.

Contribution

It systematically investigates the full four-dimensional HKB model, uncovering previously unreported dynamical regimes and bi-stability in joint action coordination.

Findings

Discovery of new dynamical regimes in the HKB model

Identification of stability boundaries for coordination patterns

Evidence of bi-stability between different coordination states

Abstract

In 1985 Haken, Kelso and Bunz proposed a system of coupled nonlinear oscillators as a model of rhythmic movement patterns in human bimanual coordination. Since then, the Haken-Kelso-Bunz (HKB) model has become a modelling paradigm applied extensively in all areas of movement science, including interpersonal motor coordination. However all previous studies have followed the line of analysis based on the slow varying amplitude and rotating wave approximations. These approximations lead to a reduced system comprised of a single differential equation representing the evolution of the relative phase of the two coupled oscillators. Here we take a different approach and systematically investigate the behaviour of the HKB model in the full four-dimensional state space. We perform detailed numerical bifurcation analyses and reveal that the HKB model supports previously unreported dynamical regimes as well as bi-stability between a variety of coordination patterns. Furthermore, we identify the stability boundaries of distinct coordination regimes in the model and discuss the applicability of our findings to interpersonal coordination and other joint-action tasks.