A model for phase transitions in human hand movements during multifrequency tapping

In bimanual tapping, abrupt transitions between frequency ratios were observed when movement frequency was gradually increased. The transition routes showed individual tendencies, not necessarily in agreement with predictions derived from the sine circle map. Therefore, a more detailed theoretical model of coupled oscillators was developed. In the model the interaction function is a polynomial of coupling terms which allow for specific frequency locks. The magnitudes of these coupling terms are related to the amplitude of oscillation and the order of the frequency lock. Because increase in movement frequency is associated with a drop in amplitude, it results in differential loss of stability of the allowed frequency ratios. New frequency-locked states may be attained by detuning the stiffness parameters of the component oscillators. The model accounts for both free-running solutions and individual tendencies in transition routes. The relative weights of the coupling terms are influenced by practice and intention.