@article{38156,
  keywords = {neural networks, noninvertibility, critical curves, system   identification},
  author = {Gicquel and Anderson and Kevrekidis},
  title = {Noninvertibility and resonance in discrete-time neural networks for time-series processing},
  abstract = { We present a computer-assisted study emphasizing certain elements of the dynamics of artificial neural networks (ANNs) used for discrete time-series processing and nonlinear system identification. The structure of the network gives rise to the possibility of multiple inverses of a phase point backward in time; this is not possible for the continuous-time system from which the time series are obtained, Using a two-dimensional illustrative model in an oscillatory regime, we study here the interaction of attractors predicted by the discrete-time ANN model (invariant circles and periodic points locked on them) with critical curves. These curves constitute a generalization of critical points for maps of the interval (in the sense of Julia-Fatou); their interaction with the model-predicted attractors plays a crucial role in the organization of the bifurcation structure and ultimately in determining the dynamic behavior predicted by the neural network. (C) 1998 Published by Elsevier Science B.V. },
  year = {1998},
  journal = {Physics Letters APhysics Letters A},
  volume = {238},
  pages = {8-18},
  month = {01/1998},
  isbn = {0375-9601},
  language = {English},
}