Abstract
We propose a novel method of combining artificial neural networks (ANNs) with chaotic noise reduction techniques that captures the metric and dynamic invariants of a chaotic time series, e.g. a time series obtained by iterating the logistic map in chaotic regimes. Our results indicate that while the feedforward neural network is capable of capturing the dynamical and metric invariants of chaotic time series within an error of about 25%, ANNs along with chaotic noise reduction techniques, such as Hammel’s method or the local projective method, can significantly improve these results. This further suggests that the effort on the ANN to train data corresponding to complex structures can be significantly reduced. This technique can be applied in areas like signal processing, data communication, image processing etc.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Albano A M, Passamante A, Hediger T, Farrell M E 1992 Using neural nets to look for chaos.Physica D58: 1–9
Cawley R and Hsu G H 1992 Local projection method for noise reduction in chaotic maps and flows.Phys. Rev. A46: 3057–3066
Chandra Shekara Bhat C, Kaimal M R 1995 Approximation of chaotic behavior using artificial neural networks.Proceedings of the Third International Seminar on Intelligent Robotic Systems, Bangalore
Chandra Shekara Bhat C, Kaimal M R 1997 Identification and reproduction of bifurcation diagram of logistic map using ANN.Proceedings of the National Conference on Neuro-Fuzzy Systems (New Delhi: Narosa)
Deco G, Schurmann B 1994 Neural learning of chaotic system behavior.IEICE Trans. Fundamentals E77-A: 1840–1845
Ginsburg I, Horn D 1992 Learning the rule of time series.Int. J. Neural Syst. 3: 167–177
Hammel S M 1990 A noise reduction method for chaotic systems.Phys. Lett. A148: 421–429
Kantz H, Schreiber T 1997Nonlinear time series analysis (Cambridge: University Press)
Nagayama I, Akamatsu N 1994 Approximation of chaotic behavior by using neural network.IEICE Trans. Inf. Syst. E77-D: 450–458
Navone H D, Ceccatto H A 1995 Learning chaotic dynamics by neural networks.Chaos, Solitons Fractals 6: 383–387
Principe J, Rathie A, Kuo J 1992 Prediction of chaotic time series with neural networks and the issue of dynamical modelling.Int. J. Bifurcation Chaos 2: 989–996
Rumelhart D E, Hinton G E, Williams R J 1986 Learning internal representations by error propagation.Parallel distributed processing: Explorations in the microstructures of cognition (eds) D E Rumelhart, J L McClelland, (Cambridge, MA: MIT Press) 1: 318–362
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Bhat, C.C.S., Kaimal, M.R. & Ramamohan, T.R. Application of chaotic noise reduction techniques to chaotic data trained by ANN. Sadhana 26, 485–494 (2001). https://doi.org/10.1007/BF02703445
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02703445