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

Avitabile, Daniele and Słowiński, Piotr and Bardy, Benoit and Tsaneva-Atanasova, Krasimira (2016) Beyond in-phase and anti-phase coordination in a model of joint action. Biological Cybernetics, 110 (2-3). pp. 201-216. ISSN 1432-0770

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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 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.

Item Type: Article
Keywords: Coupled oscillators, Dynamical system, Bifurcation analysis Coordination regimes, Numerical continuation, Parameter dependence
Schools/Departments: University of Nottingham UK Campus > Faculty of Science > School of Mathematical Sciences
Identification Number: https://doi.org/10.1007/s00422-016-0691-9
Depositing User: Eprints, Support
Date Deposited: 14 Jun 2016 07:47
Last Modified: 18 Sep 2016 11:46
URI: http://eprints.nottingham.ac.uk/id/eprint/33985

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