Gravity-dependent walk-run transition via saddle-node bifurcation and cusp catastrophe

Humans perform adaptive locomotion in diverse environments. To adapt to changes in speed, they switch their gait between walking and running. Many gait parameters suddenly change at gait transitions and the walk-to-run and run-to-walk transition speeds differ (i.e., hysteresis appears). However, the mechanism of this hysteresis remains largely unclear. With the recent momentum toward manned exploration programs, it has become increasingly important to elucidate the effects of low-gravity environments on human locomotion. Low gravity significantly alters gait transitions. In particular, the sudden changes in the gait parameters and hysteresis disappear. The mechanism of these changes in low-gravity environments also remains largely unclear. In this study, we developed a neuromechanical model to reproduce the sudden gait transitions and hysteresis under normal gravity and the smooth gait transitions and disappearance of hysteresis under low gravity, as verified by a comparison with human data. A nonlinear dynamic analysis shows that resonance induces saddle-node bifurcations, which cause the sudden gait transitions and hysteresis, and that low gravity changes the resonance such that it induces a cusp catastrophe, which causes the smooth gait transitions and disappearance of hysteresis. Our results will lead to a better understanding of human adaptation to gravity in terms of motor control, contributing to future human space activities, and provide useful insight into rehabilitation techniques.