Abstract
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.
Highlights
Exploring complex human behavior from the perspective of a dynamical system began with a historic experiment [1]
We review the applications of a dynamical system approach to human behavior, with particular regard to sports activities that require quick decision-making and appropriate execution
All trajectories are considered to represent the transition between the excited attractors, called the fractal transition between the excited attractors, to characterize the dynamics of the dissipative dynamical system excited by the temporal inputs
Summary
Exploring complex human behavior from the perspective of a dynamical system began with a historic experiment [1]. Anti-phase synchronization of the tree frogs was analyzed as a phase oscillator model [12] As another approach, the symmetric Hopf bifurcation theory based on group theory [13] was applied to investigate the synchronized pattern of three people during a sports activity [14]. A Markov chain in discrete time, which is characterized as a state transition based on the probability distribution of the state, depends only on the current state as a kind of discrete dynamics, and has been applied to baseball batting [15] and to squash [16,17] These studies examined predictions pertaining to competitive sports performance and did not explore the underlying dynamics. To explore complex human movement as a dynamical system, we introduce switching hybrid dynamical systems, which include discrete and continuous dynamics with a feedback loop
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