Abstract
Motor coordination is an important feature of intra- and inter-personal interactions, and several scenarios --- from finger tapping to human-computer interfaces --- have been investigated experimentally. In the 1980, Haken, Kelso and Bunz formulated a coupled nonlinear two-oscillator model, which has been shown to describe many observed aspects of coordination tasks. We present here a bifurcation study of this model, where we consider a delay in the coupling. The delay is shown to have a significant effect on the observed dynamics. In particular, we find a much larger degree of bistablility between in-phase and anti-phase oscillations in the presence of a frequency detuning.
Highlights
Many joint-action tasks demand some degree of movement coordination
We presented a bifurcation study of the HKB model for physically relevant parameter settings that are consistent with experimental data, and with delay in the coupling
The focus was on the effect of the delay on stable in-phase and anti-phase periodic solutions, where we considered the case when a frequency detuning is present
Summary
Many joint-action tasks demand some degree of movement coordination. the degree of movement coordination plays an important role in inter-personal interactions; e.g., it can affect the level of affiliation between interacting people [21]. In the case of (near) periodic movements the collective patterns of coordination are well captured by the properties of the relative phase, φrel, between the individual coupled oscillating subsystems [10]. We present a bifurcation study, by means of numerical continuation, of the HKB model with time delays, that investigates further and explains simulation results in [31]. Since delay differential equations can exhibit richer dynamics than ordinary differential equations, this type of study constitutes an important step towards a deeper understanding of more realistic models for motor coordination. We consider (1) with equal coupling strengths a = a1 = a2 and b = b1 = b2 This is usually regarded as a model of intra-personal coordination, such as coordination of the left and right hand of the same person; we assume an equal delay τ = τ1 = τ2.
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