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A Switching Hybrid Dynamical System: Toward Understanding Complex Interpersonal Behavior

by 1,*,†, 2,†, 3,†, 1,† and 4,†
1
Research Center of Health, Physical Fitness, and Sports, Nagoya University, Nagoya 464-8601, Japan
2
Graduate School of Education, University of Yamanashi, Kofu 400-8510, Japan
3
Graduate School of Education, Tokyo Gakugei University, Tokyo 184-8501, Japan
4
Division of Applied Physics, Graduate School of Engineering, Hokkaido University, Sapporo 063-8628, Japan
*
Author to whom correspondence should be addressed.
These authors contributed equally to this work.
Appl. Sci. 2019, 9(1), 39; https://doi.org/10.3390/app9010039
Received: 28 October 2018 / Revised: 14 December 2018 / Accepted: 20 December 2018 / Published: 22 December 2018
(This article belongs to the Section Applied Physics)
Complex human behavior, including interlimb and interpersonal coordination, has been studied from a dynamical system perspective. We review the applications of a dynamical system approach to a sporting activity, which includes continuous, discrete, and switching dynamics. Continuous dynamics identified switching between in- and anti-phase synchronization, controlled by an interpersonal distance of 0.1 m during expert kendo matches, using a relative phase analysis. In the discrete dynamical system, return map analysis was applied to the time series of movements during kendo matches. Offensive and defensive maneuvers were classified as six coordination patterns, that is, attractors and repellers. Furthermore, these attractors and repellers exhibited two discrete states. Then, state transition probabilities were calculated based on the two states, which clarified the coordination patterns and switching behavior. We introduced switching dynamics with temporal inputs to clarify the simple rules underlying the complex behavior corresponding to switching inputs in a striking action as a non-autonomous system. As a result, we determined that the time evolution of the striking action was characterized as fractal-like movement patterns generated by a simple Cantor set rule with rotation. Finally, we propose a switching hybrid dynamics to understand both court-net sports, as strongly coupled interpersonal competition, and weakly coupled sports, such as martial arts. View Full-Text
Keywords: interpersonal coordination; competition; dynamical systems; discrete dynamics; continuous dynamics; sporting activity interpersonal coordination; competition; dynamical systems; discrete dynamics; continuous dynamics; sporting activity
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Yamamoto, Y.; Kijima, A.; Okumura, M.; Yokoyama, K.; Gohara, K. A Switching Hybrid Dynamical System: Toward Understanding Complex Interpersonal Behavior. Appl. Sci. 2019, 9, 39.

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