Switching Dynamics Between Two Movement Patterns Varies According to Time Interval

Abstract

This study investigated the regularity that characterizes the behavior of dissipative dynamical systems excited by external temporal inputs for pointing movements. Right-handed healthy male participants were asked to continuously point their right index finger at two light-emitting diodes (LEDs) located in the oblique left and right directions in front of them. These movements were performed under two conditions: one in which the direction was repeated and one in which the directions were switched on a stochastic basis. These conditions consisted of 12 tempos (30, 36, 42, 48, 51, 54, 57, 60, 63, 66, 69, and 72 beats per minute). Data from the conditions under which the input pattern was repeated revealed two different trajectories in hyper-cylindrical state space M, whereas the conditions under which the inputs were switched induced transitions between the two trajectories, which were considered to be excited attractors. The transitions between the two excited attractors were characterized by a self-similar structure. Moreover, the correlation dimensions increased as the tempos increased. These results suggest a relationship of D ∝ 1/T (T is the switching-time length; i.e. the condition) between temporal input and pointing behavior and that continuous pointing movements are regular rather than random noise.

Inverse Proportional Relationship Between Switching-Time Length and Fractal-Like Structure for Continuous Tracking Movement

“…this is considered an excited attractor. Recent studies based on this dynamical systems theory, for example not only the physical phenomenon [Arecchi et al, 1986;Constantin et al, 1991;Maas et al, 1997;Matias et al, 1997;Mestl et al, 1997;Schmiegel & Eckhardt, 1997;Tanii et al, 1999;Tanii et al, 1991] but also human movement [Hirakawa et al, 2016;Suzuki & Yamamoto, 2015;Yamamoto & Gohara, 2000], have revealed that the spatiotemporal structure in various natural phenomena is fractal-like and/or self-similar. These studies on human movement entailed tasks in which participants switched several different movement patterns continuously with the external inputs being abruptly switched.…”

“…This theoretical framework is detailed in the next section. Figure 1 shows schematics highlighting the difference between autonomous and nonautonomous systems [Hirakawa et al, 2016]. For instance, Figs.…”

“…1(a) and 1(b) show autonomous systems. [Hirakawa et al, 2016]. See the body of the text for further details.…”

“…the correlation dimension, are closely related to each other. Furthermore, a regular relationship exists between T and the fractal dimension [Hirakawa et al, 2016].…”

“…Until now, few previous studies have been conducted in which human movement has been analyzed [Hirakawa et al, 2016]; hence, accumulating examinations of various human movements within the context of nonautonomous dynamical systems theory is essential. For example, Hirakawa et al [2016] analyzed continuous trajectories of a fingertip in pointing movements toward left and right directions. However, such a task might be considered a discrete task, because it involves a reaching movement toward two preset locations.…”