Deterministic variability and stability in detuned bimanual rhythmic coordination

We examined the effects of crossing different degrees of cooperation and competition on inphase and antiphase 1:1 frequency locked coordination of left- and right-hand-oscillated pendulums. Degree of cooperation was manipulated through the joint frequency of oscillation specified by a metronome (the higher the frequency, the weaker the cooperation), and degree of competition by length (and, therefore, preferred frequency) differences between the two pendulums (the greater the difference, the stronger the competition). Increasing competition was accompanied by either decreasing cooperation (for six participants) or increasing cooperation (for six different participants). On each trial, a participant attempted to produce a steady-state phase relation phi for a given combination of competition and cooperation. Numerical simulations of the extended Haken-Kelso-Bunz (HKB) equation were used to predict (a) the patterns of shift in phi from either 0 or pi radians due to the different competition-cooperation relations and (b) the patterns of variability in phi. It was expected that the HKB equation would be successful in respect to (a), which it was, but not in respect to (b). The observed failure to confirm (b) was expected from the variability due to the different nonharmonic dynamics of the component oscillators, a source of variability not included in the HKB equation. The experimental results together with simulations and analyses of the phase-plane trajectories of the component oscillators suggest the operation of deterministic in addition to stochastic variability in the phase relation of contralateral limbs.