We examine the identifiability of a nonlinear state space system
under general assumptions. The discrete time evolution of the state is
generated by a recurrent Elman network. For a large set of Elman
networks we determine the class of observationally equivalent minimal
systems, i.e., minimal systems that exhibit the same input-output
behavior.The authors are grateful for
discussions with M. Deistler and D. Bauer. A.A. Al-Falou was funded by
the ERNSI network within the European Union program Training and Mobility
of Researchers (TMR). D. Trummer was funded by the FWF (Austrian Science
Fund). We thank an anonymous referee for helpful comments and
suggestions.