Renormalization group analysis of a quivering string model of posture control

Scaling concepts and renormalization group methods are applied to a simple linear model of human posture control consisting of a trembling or quivering string subject to damping and restoring forces. The string is driven by uncorrelated white Gaussian noise, intended to model the corrections of the physiological control system. We find that adding a weak quadratic nonlinearity to the posture control model opens up a rich and complicated phase space (representing the dynamics) with various nontrivial fixed points and basins of attraction. The transition from diffusive to saturated regimes of the linear model is understood as a crossover phenomenon, and the robustness of the linear model with respect to weak nonlinearities is confirmed. Correlations in posture fluctuations are obtained in both time and space domains. There is an attractive fixed point identified with falling. The scaling of the correlations in the front-back displacement, which can be measured in the laboratory, is predicted for both large-separation (along the string) and long-time regimes of posture control.