Steady-state and perturbed rhythmical movements: A dynamical analysis.

Abstract

This study examined rhythmic finger movements in the steady state and when momentarily perturbed in order to derive their qualitative dynamical properties. Movement frequency, amplitude, and peak velocity were stable under perturbation, signaling the presence of an attractor, and the topological dimensionality of that attractor was approximately equal to one. The strength of the attractor was constant with increasing movement frequency, and the Fourier spectra of the steady-state trials showed an alternating harmonic pattern. These results are consistent with a previously derived nonlinear oscillator model. However, the oscillation was phase advanced by perturbation overall, and a consistent phase-dependent, phase-shift pattern occurred, which is inconsistent with the model. The overall phase advance also shows that any central pattern generator responsible for generating the rhythm must be nontrivially modulated by the limb being controlled.

Deterministic and stochastic features of rhythmic human movement

“…(9) was fitted to the three types of data shown in Fig. 6a; here, x refers to the recorded position and y to the corresponding velocity (11) Figure 6b shows that this model fitting yields phase portraits that are very similar to the reconstructed ones in the case of forearm and wrist cycling (left and middle panels), supporting earlier studies of Kay et al (1987Kay et al ( , 1991 and Beek et al (1996). For the tapping data, however, the results turn out to be quite poor because we ignored most prominent features like asymmetry and anchoring in constructing the model according to Eq.…”

“…Using averaging methods from the theory of nonlinear oscillators, such as the slowly-varying amplitude approximation and harmonic balance analysis, Kay et al (1987Kay et al ( , 1991 derived second-order nonlinear differential equations that mimicked experimentally observed amplitude-frequency relation and the phase response characteristics of rhythmic finger and wrist movements. In particular, these selfsustaining oscillators included weak dissipative nonlinearities that stabilized the limit cycle and caused a drop of amplitude (accounted for by a Rayleigh term) and an increase in peak velocity (accounted for by a van der Pol term) with increasing movement tempo (i.e., frequency).…”

Laterally focused attention modulates asymmetric coupling in rhythmic interlimb coordination

“…Perturbation at this movement phase does not invoke large sudden changes in kinetic energy, while allowing an equally adequate estimation of relaxation time as at other movement phases (cf. Kay, Saltzman, & Kelso, 1991). The perturbation was applied randomly between the 12th and the 17th cycle of the trial, with the moment of its onset being extrapolated online from the eight preceding movement cycles.…”

Transfer of learning between unimanual and bimanual rhythmic movement coordination: transfer is a function of the task dynamic

“…The model predicted results both from movement studies (e.g. Kay, Kelso, Saltzman and Schöner 1987;Kay, Saltzman and Kelso 1991;Kelso 1984;Schmidt, Carello and Turvey 1990) and from perceptual judgment studies that had investigated both vision (Bingham, Schmidt and Zaal 1999;Bingham, Schmidt, Shull and Collins 2001;Collins and Bingham 2001;Zaal, Bingham and Schmidt 2000) and proprioception (Wilson, Craig and Bingham 2003). It is this model that motivated the current study because it generates predictions about how learning one version of this task should generalise to another version.…”