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

Avitabile, Daniele; S?owi?ski, Piotr; Bardy, Benoit; Tsaneva-Atanasova, Krasimira

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.

Citation

Avitabile, D., Słowiński, P., Bardy, B., & Tsaneva-Atanasova, K. (in press). Beyond in-phase and anti-phase coordination in a model of joint action. Biological Cybernetics, 110(2-3), https://doi.org/10.1007/s00422-016-0691-9

• Journal Article Type: Article
• Acceptance Date: May 27, 2016
• Online Publication Date: Jun 8, 2016
• Deposit Date: Jun 14, 2016
• Publicly Available Date: Jun 14, 2016
• Journal: Biological Cybernetics
• Print ISSN: 0340-1200
• Electronic ISSN: 1432-0770
• Publisher: Springer Verlag
• Peer Reviewed: Peer Reviewed
• Volume: 110
• Issue: 2-3
• DOI: https://doi.org/10.1007/s00422-016-0691-9
• Keywords: Coupled oscillators, Dynamical system, Bifurcation analysis Coordination regimes, Numerical continuation, Parameter dependence
• Public URL: https://nottingham-repository.worktribe.com/output/796085
• Publisher URL: http://dx.doi.org/10.1007/s00422-016-0691-9
• Contract Date: Jun 14, 2016