Parameter uncertainties in models of equivariant dynamical systems

Abstract

We examine the advantages of using equivariant versus nonequivariant phenomenological models for chaotic systems that possess an inversion symmetry. Numerical experiments used the minimum description length (MDL) criteria for model selection. They indicated that the selection between equivariant versus nonequivariant models should be made on an a priori basis. We also examine the relationship between the optimal truncation accuracy of the parameters of the model (as predicted by the MDL criteria) and the true uncertainty in the parameters of the model. Numerical experiments indicate that the true uncertainties are poorly approximated by the optimal truncation accuracy. They also indicate that the true uncertainties may be useful for determining the presence of an inversion symmetry in reconstructed attractors.