Funato Tetsuro, Aoi Shinya, Tomita Nozomi, Tsuchiya Kazuo
Department of Mechanical Engineering and Intelligent Systems, The University of Electro-communications, 1-5-1 Chofugaoka, Chofu, Tokyo 182-8585, Japan; JST, CREST, 5 Sanbancho, Chiyoda-ku, Tokyo 102-0075, Japan.
Department of Aeronautics and Astronautics, Kyoto University, Kyoto daigaku-Katsura, Nishikyo-ku, Kyoto 615-8540, Japan; JST, CREST, 5 Sanbancho, Chiyoda-ku, Tokyo 102-0075, Japan.
R Soc Open Sci. 2016 Jan 6;3(1):150570. doi: 10.1098/rsos.150570. eCollection 2016 Jan.
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.
人体安静站立时会伴随着身体摆动。已知这种身体摆动的幅度比简单噪声效应所预测的要大，并且摆动特征会因神经系统疾病而改变。这种较大的摆动被认为源于长时间无控制（间歇控制）的非线性控制，并且预计这种非线性控制系统会出现分岔。稳定性依赖转变的存在使得动态反应取决于环境的稳定性，并且可以解释伴随某些神经系统疾病的摆动特征变化。本研究分析了诱导转变的系统模型的特征，并讨论人体站立是否反映了这样一种机制。在系统模型的数学分析中，具有积分控制的（类似间歇控制的）非线性控制被证明会出现霍普夫分岔。此外，从带有噪声的系统模型的解析解可知，噪声起到平滑分岔点附近摆动增大的作用。将该解与在不同稳定性地板上测量的人体站立摆动进行比较。通过定量比较人体观测和模型预测之间的控制参数，摆动增大如模型分析所预测的那样出现。
