ArticleBiological cybernetics2016
Beyond in-phase and anti-phase coordination in a model of joint action.
Article in Biological cybernetics, 2016. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 13 papers.
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Who cites it
13 citing papers in PubMed.
- Optimal phase-selective entrainment of heterogeneous oscillator ensembles.SIAM journal on applied dynamical systems · 2023Article
- Intra- and inter-individual variability in the underwater pull-out technique in 200 m breaststroke turns.PloS one · 2023Article
- Involvement of global coordinative structure in achieving the local pendulum swinging task.PloS one · 2022Article
- Cross-frequency coupling explains the preference for simple ratios in rhythmic behaviour and the relative stability across non-synchronous patterns.Philosophical transactions of the Royal Society of London. Series B, Biological sciences · 2021Article
- The Haken-Kelso-Bunz (HKB) model: from matter to movement to mind.Biological cybernetics · 2021Article
- Two dimensionless parameters and a mechanical analogue for the HKB model of motor coordination.Biological cybernetics · 2021Article
- Unifying Large- and Small-Scale Theories of Coordination.Entropy (Basel, Switzerland) · 2021Article
- A Re-Appraisal of the Effect of Amplitude on the Stability of Interlimb Coordination Based on Tightened Normalization Procedures.Brain sciences · 2020Article
- Coordination Dynamics: A Foundation for Understanding Social Behavior.Frontiers in human neuroscience · 2020Article
- Delayed feedback embedded in perception-action coordination cycles results in anticipation behavior during synchronized rhythmic action: A dynamical systems approach.PLoS computational biology · 2019Article
- Unintentional force changes in cyclical tasks performed by an abundant system: Empirical observations and a dynamical model.Neuroscience · 2017Article
- Entrainment and synchronization in networks of Rayleigh-van der Pol oscillators with diffusive and Haken-Kelso-Bunz couplings.Biological cybernetics · 2016Article
- Anisotropy and Antagonism in the Coupling of Two Oscillators: Concepts and Applications for Between-Person Coordination.Frontiers in psychology · 2016Article
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Authors and funding
4 authors.
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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.
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