### 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.

Original language | English (US) |
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Pages (from-to) | 8-18 |

Number of pages | 11 |

Journal | Physics Letters, Section A: General, Atomic and Solid State Physics |

Volume | 238 |

Issue number | 1 |

DOIs | |

State | Published - Jan 26 1998 |

### All Science Journal Classification (ASJC) codes

- Physics and Astronomy(all)

### Keywords

- Critical curves
- Neural networks
- Noninvertibility
- System identification

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## Cite this

*Physics Letters, Section A: General, Atomic and Solid State Physics*,

*238*(1), 8-18. https://doi.org/10.1016/S0375-9601(97)00753-6