Data from: Smooth enlargement of human standing sway by instability due to weak reaction floor and noise

Human quiet standing is accompanied by body sway. The amplitude of this body sway is known to be larger than would be predicted from simple noise effects, and sway characteristics are changed by neurological disorders. This large sway is thought to arise from nonlinear control with prolonged periods of no control (intermittent control), and a nonlinear control system of this kind has been predicted to exhibit bifurcation. The presence of stability-dependent transition enables dynamic reaction that depends on the stability of the environment, and can explain the change in sway characteristics that accompanies some neurological disorders. This research analyzes the characteristics of a system model that induces transition, and discusses whether human standing reflects such a mechanism. In mathematical analysis of system models, (intermittent control-like) nonlinear control with integral control is shown to exhibit Hopf bifurcation. Moreover, from the analytical solution of the system model with noise, noise is shown to work to smooth the enlargement of sway around the bifurcation point. This solution is compared with measured human standing sway on floors with different stabilities. By quantitatively comparing the control parameters between human observation and model prediction, enlargement of sway is shown to appear as predicted by the model analysis.

人类静息站立时会伴随身体摆动。已知此类身体摆动的幅度大于单纯噪声效应所能预测的水平，且摆动特性会因神经系统疾病发生改变。学界认为这类大幅摆动源于存在长时间无控制阶段的非线性控制（间歇控制（intermittent control）），且此类非线性控制系统被预测会出现分岔（bifurcation）现象。依赖于稳定性的状态转变可使系统产生依赖环境稳定性的动态响应，这也能够解释部分神经系统疾病所伴随的身体摆动特性变化。本研究分析了可诱发状态转变的系统模型的特性，并探讨人类静立姿态是否符合该机制。在系统模型的数学分析中，带有积分控制的类间歇控制非线性控制系统被证明会出现霍夫分岔（Hopf bifurcation）。此外，通过含噪声的系统模型解析解可知，噪声能够平滑分岔点附近身体摆动幅度的放大过程。将该解析解与不同稳定性地板上测得的人类静立身体摆动数据进行对比。通过定量对比人类观测数据与模型预测的控制参数，结果表明身体摆动幅度的放大现象与模型分析的预测结果一致。