Advantages of Rhythmic Movements at Resonance: Minimal Active Degrees of Freedom,Minimal Noise,and Maximal Predictability

Using time delay embedding, the authors applied phase space reconstruction to the time series of rhythmic movements of a hand-held pendulum. Subjects (N = 6) produced the manual oscillations about the wrist at the pendulum's resonant frequency and at a higher and a lower frequency. The number of active degrees of freedom required to capture the dynamics of the rhythmic behavior was 3 for the resonant frequency and 4 for each of the nonresonant frequencies. The residual high-dimensional noise was similarly lowest for the resonant frequency. Whereas 33% and 20%, respectively, of the vectors in the phase spaces of the dynamics higher and lower than resonance were unpredictable, only 12% were unpredictable at resonance. Finally, the predictability of the evolving dynamics extended farther into the future for oscillations at the resonant frequency. At resonance, the prediction horizon was 5 times farther than the prediction horizon for the higher than resonance behavior and 2.5 times farther than that for the lower than resonance behavior. The results suggest that, in pendular oscillations of a limb or limb segment, attunement of the central nervous system to the resonant frequency minimizes the variables to be controlled and maximizes the predictability of the rhythmic movement's chaotic dynamics.