MODELING THE CONTROL OF ISOMETRIC FORCE PRODUCTION WITH PIECE-WISE LINEAR, STOCHASTIC MAPS OF MULTIPLE TIME-SCALES

In human movement, the large number of system degrees of freedom at different levels of analysis of the system, joints, muscles, motor units, cells etc, naturally affords complexity and adaptability in action. It also leads to variability in movement and its outcome, even in intentional efforts to reproduce the same movement or action goal. An example is continuous isometric force output to a constant force level where the amount and structure of force variability changes with information available, force level and individual differences. In this paper we model the control of isometric force production with piece-wise linear stochastic maps of multiple time scales. At the core of our model is a piecewise linear function, depending on three parameters that can be estimated from the observed data that is perturbed by additive Gaussian noise at a given level. The result of the stochastic forcing is that outside of a threshold interval the system behaves like a discrete Ornstein-Uhlenbeck process and inside it performs a Brownian motion. The model is shown to simulate the basic findings of the structure of human force variability that decreasing variability is correlated with increased dynamical complexity as measured with the "Approximate Entropy (ApEn)" statistic.