PARAMETER UNCERTAINTIES IN MODELS OF EQUIVARIANT DYNAMICAL-SYSTEMS

We examine the advantages of using equivariant versus nonequivariant p henomenological models for chaotic systems that possess an inversion s ymmetry. Numerical experiments used the minimum description length (MD L) criteria for model selection. They indicated that the selection bet ween equivariant versus nonequivariant models should be made on an a p riori basis. We also examine the relationship between the optimal trun cation accuracy of the parameters of the model (as predicted by the MD L criteria) and the true uncertainty in the parameters of the model. N umerical experiments indicate that the true uncertainties are poorly a pproximated by the optimal truncation accuracy. They also indicate tha t the true uncertainties may be useful for determining the presence of an inversion symmetry in reconstructed attractors.