Reconstruction of the parameter spaces of dynamical systems - art. no. 056215

Parameter variations in the equations of motion of dynamical systems are id entified by time series analysis. The information contained ill time series data is transformed and compressed to feature vectors. The space of featur e vectors is an embedding for the unobserved parameters of the system. We s how that the smooth variation of d system parameters can lead to paths of f eature vectors on smooth d-dimensional manifolds in feature space, provided the latter is high-dimensional enough. The number of varying parameters an d the nature of their variation can thus be identified. The method is illus trated using numerically generated data and experimental data from electrom otors. Complications arising from bifurcations in deterministic dynamical s ystems are shown to disappear for slightly noisy systems.