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 analyses 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.人体静立站立时会伴随身体晃动。现有研究证实，此类身体晃动的幅度大于仅由简单噪声效应所能预测的数值，且晃动特征会因神经系统疾病发生改变。这种幅度异常增大的晃动被认为源于带有长时间无控制阶段的非线性控制——即间歇控制（intermittent control），而此类非线性控制系统理论上会表现出分岔现象。依赖于系统稳定性的分岔转变，能够实现随环境稳定性变化的动态响应，这也可以解释部分神经系统疾病患者的身体晃动特征改变。本研究针对具备分岔转变特性的系统模型展开特征分析，并探讨人体静立姿态是否遵循此类调控机制。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系统被证实会产生霍普夫分岔（Hopf bifurcation）。此外，通过对含噪声的系统模型求解解析解，发现噪声能够平滑分岔点附近的晃动幅度放大效应。将该解析解与不同稳定性地板上测得的人体静立晃动数据进行对比，通过定量比对人体观测结果与模型预测的控制参数，证实了晃动幅度的放大现象与模型分析的预测结果一致。