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. As discrete dynamics, return map analysis was applied to the time series of movements during kendo matches, and six coordination patterns were classified. Furthermore, 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.

Sex dimorphism starts during early embryogenesis and is further manifested in response to hormones during puberty. As this leads to physical divergence that is measurably different between sexes, males enjoy physical performance advantages over females within competitive sport. While this advantage is the underlying basis of the segregation into male and female sporting categories, these sex-based categories do not account for transgender persons who experience incongruence between their biological sex and their experienced gender identity. Accordingly, the International Olympic Committee determined criteria by which a transgender woman may be eligible to compete in the female category, requiring total serum testosterone levels to be suppressed below 10 nmol/L for at least 12 months prior to and during competition. Whether this regulation removes the male performance advantage has not been collectively scrutinized. Here, we aim to review how differences in biological characteristics between biological males and females affect sporting performance and assess whether evidence exists to support the assumption that testosterone suppression in transgender women removes the male performance advantage. In this review, we report that the performance gap between males and females amounts to 10-50% depending on sport. The performance gap is more pronounced in sporting activities relying on muscle mass and strength, particularly in the upper body. Longitudinal studies examining the effects of testosterone suppression on muscle mass and strength in transgender women consistently show very modest changes, where the loss of lean body mass, muscle area and strength typically amounts to approximately 5% after 1 year of treatment. Thus, current evidence shows that the biological advantage enjoyed by transgender women is only minimally reduced when testosterone is suppressed. Sports organizations may therefore be compelled to reassess current policies regarding participation of transgender women in the female category of sport.