Are frequency-induced transitions in rhythmic coordination mediated by a drop in amplitude?

The coordination of rhythmic movements is characterized by attraction to stable modes as well as by loss of stability due to the manipulation of external control parameters. For isochronous coordination between two oscillating components, frequency-induced transitions from antiphase to inphase coordination are frequently observed. Such transitions have been understood on the basis of a dynamical model, the HKB model, consisting of both a potential function for relative phase and a description of the oscillating limbs in terms of nonlinearly coupled limit cycle oscillators. According to the latter aspect of this model, the loss of stability of the antiphase pattern, which precedes the transition to the inphase pattern, is mediated by the decrease in movement amplitude that occurs when the movement frequency is scaled up. This amplitude-based transition mechanism was examined experimentally in the context of a unimanual tracking task. Subjects were instructed to maintain a prescribed amplitude, while tracking an oscillating visual stimulus in either the inphase or the antiphase mode. Three different movement amplitudes were used to examine the prediction that larger amplitudes lead to more stable coordination. When the frequency of oscillation was gradually increased, transitions from antiphase to inphase coordination were observed in the majority of the trials, despite constant or sometimes even slightly increasing amplitudes. No significant effects of amplitude on pattern stability, as indicated by the variability of relative phase and by the critical frequency, were observed. To the extent that these findings can be generalized beyond the present task domain, they suggest that frequency-induced transitions in coordinated rhythmic movements may not be mediated by a drop in amplitude and that alternative directions in modeling may have to be considered.