A novel stretching and folding characterization method based on geometrical and physiological traits of chaotic and intermittent tracking signals

– The specification of stretching and folding properties, particularly in time series, is of substantial interest. This study is sought to perceive the relationship between stretching and folding and irregular discontinuities in hand motion trajectories during target tracking tasks. In this regard, a new method is proposed based on compiling physiological characteristics and hand motion dynamics’ geometrical traits. Thus, five tracking conditions are designed in which participants are instructed to track different target motion patterns. In these experiments, sinusoidal and trapezoidal target movements with frequencies of 0.1 and 0.3 Hz, as well as pseudo-periodic target motion created by summing two sinusoids with frequencies of 0.117 and 0.278 Hz, are used as visual targets. The results illustrate that nonuniform discontinuities are noticeable properties of the hand motion trajectory. Also, the largest Lyapunov exponent, correlation dimension, and fractal dimension corroborate that the tracking attractor is low-dimensional and chaotic. Moreover, the results are compared with the curvature-based method, and its modified version is presented by taking advantage of the proposed method. As a result, through the suggested method, stretching and folding points are well discerned regardless of discontinuities. This method can deal with the systems with intermittency in both times-and state space.