Robustness to temporal constraint explains expertise in ball-over-net sports.

The present study investigated motor expertise in interpersonal competitive ball-over-net sports in terms of a dynamical system with temporal input. In a theoretical framework, the behavior of the system is characterized by a fractal-like structure according to switching input, which changes uniquely according to the duration of input and internal parameter of the system. We investigated periodic movements, in which the player executed a forehand or backhand stroke repeatedly, and continuous switching movements, in which the player continuously switched between two movement patterns corresponding to hitting the ball under two ball directions and with six temporal constraint conditions during a table tennis rally. In the periodic movement, we observed two limit-cycle attractors corresponding to each direction in the phase space independent of temporal constraint or skill level. Conversely, in the continuous switching movement, a transition in trajectories between the two limit-cycle attractors was observed in the phase space, and this transition was characterized by a fractal-like structure. The fractal-like structure moved closer to the random structure as temporal constraint increased independent of skill level. However, the temporal constraint condition closest to the random structure was higher for the advanced players than for the novices, indicating that robustness to the temporal constraint was higher for the advanced players than for the novices. Our results suggest that motor expertise in interpersonal competitive ball-over-net sports is more robust to temporal constraints with various inputs.