Beyond in-phase and anti-phase coordination in a model of joint action
Springer Verlag (Germany)
This is the final version of the article. Available from Springer Verlag via the DOI in this record.
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 a line of analysis based on slowly varying amplitudes and rotating wave approximations. These approximations lead to a reduced system, consisting of a single differential equation representing the evolution of the relative phase of the two coupled oscillators: the HKB model of the relative phase. Here we take a different approach and systematically investigate the behaviour of the HKB model in the full four-dimensional state space and for general coupling strengths. We perform detailed numerical bifurcation analyses and reveal that the HKB model supports previously unreported dynamical regimes as well as bistability 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.
The authors would like to thank Ed Rooke (University of Bristol, UK) for initial discussions on the HKB model analysis and Pablo Aguirre (Universidad Tecnica Federico Santa Maria, Chile) for helpful discussions on the global transition in the single HKB oscillator. This work was funded by the European Project AlterEgo FP7 ICT 2.9 - Cognitive Sciences and Robotics, Grant Number 600610. The research of KT-A was supported by grants EP/L000296/1 and EP/N014391/1 of the Engineering and Physical Sciences Research Council (EPSRC).
This is an open access article.
First Online: 08 June 2016, pp. 1 - 16