Noninvertibility and resonance in discrete-time neural networks for time-series processing |
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| Institution: | 1. Laboratory of Energy-Electric and Electronic Systems, Department of Physics, Faculty of Science, University of Yaoundé I, P.O. Box 812 Yaoundé, Cameroon;2. Galenic Pharmacy and pharmaceutical legislation Laboratory, Faculty of Medicine and Biomedical Sciences, Cameroon;3. Department of physics, Faculty of Science, University of Yaoundé I, P.O. Box 812 Yaoundé, Cameroon;4. Unité de recherche de Matière Condensée, d’Electronique et de Traitement du signal (URMACETS), Department of Physics, University of Dschang. P.O. Box 67 Dschang, Cameroon;5. Department of Physics, Faculty of Science, Moulay Ismael University of Meknes, Morroco;6. Department of Physics, Higher Teacher Training College Yaoundé, University of Yaoundé I Cameroon;7. Centre d’Excellence Africain des Technologies de l’Information et de la Communication (CETIC) Université de Yaoundé I, Cameroon;1. Department of Chemical and Environmental Engineering, Faculty of Engineering, University Putra Malaysia, 43400 Serdang, Malaysia;2. Institute of Advanced Technology, University Putra Malaysia, 43400 Serdang, Malaysia;3. Department of Chemical Engineering, Faculty of Engineering, University of Malaya, 50603 Kuala Lumpur, Malaysia;4. Global Research and Technology Centre of Scomi Oiltools Sdn. Bhd., 40105, Selangor, Malaysia |
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| 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. |
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