Detecting changes in the basin of attraction of a dynamical system: Application to the postural restoring system

Abstract

a b s t r a c tA method that provides a three-dimensional representation of the basin of attraction of a dynamical system from experimen tal data was applied to the problem of dynamic balance restoration. The method is based on the density of the data on the phase space of the system under study and makes use of modeling and numerical curve fitting tools. For the dynamical system of balance restora tion, the shape and the size of the basin of attractio n depend on the dynamics of the postural restoring mechanisms and contain important information regarding the biomechanical, as well as the neuromuscular condition of the individual. The aim of this work was to examine the ability of the method to detect, through the observed changes in the shape and/or the size of the calculated basins of attraction, (a) the inherent differences between different systems (in the current app lication, postural restoring systems of different individuals) and (b) induced chan ges in the same system (the postural restoring system of an individual). The results of the study confirm the validity of the method and furthermore justify its robustness.

Modelling Heart Rate Kinetics

“…The numerical minimization of f ( λ ) was carried out the present study by numerical optimization [ 36 , 37 ] and more specifically by application of the Levenberg—Marquardt algorithm (LMA) [ 38 , 39 ]. This algorithm, also known as the damped least-squares (DLS) method, interpolates between the Gauss-Newton and the gradient descent methods and is a very popular algorithm used in many numerical applications.…”