Chaotic features of rhythmic joint movement

The purpose of this study is to show the chaotic features of rhythmic joint movement (elbow bending and stretching exercises) using a reconstructed phase portrait, fractal dimension, and first Lyapunov exponent. The subjects were seven male students who were right-handed. Depending on the experimental conditions, one (or both) elbow angle(s) was (were) measured by one (or two) goniometer(s). Single-forearm movements were recorded for the right arm and the left arm separately. After that, they performed in-phase movements with both arms followed by anti-phase movements. All sessions started with unpaced movements at a personal tempo and amplitude. This trial was followed by six trials that were paced by signals from a personal computer. Pacing was provided for six different frequencies (1, 2, 3, 4, 5, and 6 Hz) presented in random order. When the frequency of the pace increased, the fractal dimension and first Lyapunov exponent tended to increase. Moreover, the first Lyapunov exponent obtained positive values for all of the observed data. These results indicate that there is chaos in rhythmic joint movement and that the larger the frequency, the more chaotic the joint movement becomes.