Deterministic variability and stability in detuned bimanual rhythmic coordination

We examined the effects of crossing different degrees of cooperation and co mpetition on inphase and antiphase 1:1 frequency locked coordination of lef t- and right- hand-oscillated pendulums. Degree of cooperation was manipula ted through the joint frequency of oscillation specified by a metronome (th e higher the frequency, the weaker the cooperation), and degree of competit ion 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 (fo r six participants) or increasing cooperation (for six different participan ts). On each trial, a participant attempted to produce a steady-state phase relation phi for a given combination of competition and cooperation, Numer ical 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 success ful in respect to (a), which it was, but not in respect to (b). The observe d failure to confirm (b) was expected from the variability due to the diffe rent nonharmonic dynamics of the component oscillators, a source of variabi lity not included in the HKB equation. The experimental results together wi th simulations and analyses of the phase-plane trajectories of the componen t oscillators suggest the operation of deterministic in addition to stochas tic variability in the phase relation of contralateral limbs. (C) 2001 Publ ished by Elsevier Science B.V.