Discrete- vs continuous-time nonlinear signal processing attractors, transitions and parallel implementation issues

R. Rico Martinez, I. G. Kevrekidis, M. C. Kube, J. L. Hudson

Research output: Chapter in Book/Report/Conference proceedingConference contribution

4 Scopus citations

Abstract

Artificial neural networks (ANNs) are often used for short term discrete time prediction of experimental data. In this paper we focus on the capability of such networks to identify long term behavior and, in particular, observed bifurcations correctly. The usual discrete time mapping approach is (precisely because of its discrete nature) often incapable of reproducing observed bifurcation sequences. If the interest is only in periodic or temporally more complicated behavior, a Poincare map extracted from the experimental time series can be used to circumvent this problem. A complete dynamic picture including bifurcations of steady states can, however, only be captured by a continuous-time model. We present ANN configurations which couple a 'nonlinear principal component' network for data preprocessing with (a) a composite ANN based on a simple explicit integrator scheme and (b) a recurrent ANN based on an implicit integrator scheme. These ANNs are able to correctly reconstruct bifurcation diagrams based on experimental data from the electrodissolution of metals in acidic solutions. We also discuss some issues of parallel implementation of the training algorithm.

Original languageEnglish (US)
Title of host publicationAmerican Control Conference
Editors Anon
PublisherPubl by IEEE
Pages1475-1479
Number of pages5
ISBN (Print)0780308611
StatePublished - Dec 1 1993
EventProceedings of the 1993 American Control Conference Part 3 (of 3) - San Francisco, CA, USA
Duration: Jun 2 1993Jun 4 1993

Publication series

NameAmerican Control Conference

Other

OtherProceedings of the 1993 American Control Conference Part 3 (of 3)
CitySan Francisco, CA, USA
Period6/2/936/4/93

All Science Journal Classification (ASJC) codes

  • Electrical and Electronic Engineering

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  • Cite this

    Martinez, R. R., Kevrekidis, I. G., Kube, M. C., & Hudson, J. L. (1993). Discrete- vs continuous-time nonlinear signal processing attractors, transitions and parallel implementation issues. In Anon (Ed.), American Control Conference (pp. 1475-1479). (American Control Conference). Publ by IEEE.