ESTIMATION OF THE LYAPUNOV SPECTRUM FROM ONE-DIMENSIONAL OBSERVATIONS USING NEURAL NETWORKS

Authors

  • Vladimir Golovko

DOI:

https://doi.org/10.47839/ijc.2.2.201

Keywords:

Lyapunov spectrum, Multilayer Neural Networks, Chaotic processes, Dynamical system

Abstract

This paper discusses the neural network approach for computing of Lyapunov spectrum using one dimensional time series from unknown dynamical system. Such an approach is based on the reconstruction of attractor dynamics and applying of multilayer perceptron (MLP) for forecasting the next state of dynamical system from the previous one. It allows for evaluating the Lyapunov spectrum of unknown dynamical system accurately and efficiently only by using one observation. The results of experiments are discussed.

References

I. Prigogine. The End of Certainty: Time, Chaos, and the New Laws of Nature. The Free Press, N.Y., 1997, 240p.

H. Kantz, T. Schreiber. Nonlinear time series analysis. Cambridge, Cambridge University Press, 1997.

V. Golovko. From Neural Networks to Intelligent Systems: Selected Aspects of Training. Application and Evolution // chapter of NATO book Limitations and Future Trends in Neural Computation. - Amsterdam: IOS Press, 2003. - 25 p.

V. Golovko, Y. Savitsky, N. Maniakov. Neural Networks for Signal Processing in Measurement Analysis and Industrial Applications: the Case of Chaotic Signal Processing // chapter of NATO book Neural networks for instrumentation, measurement and related industrial applications. - Amsterdam: IOS Press, 2003, pp. 119-143.

F. Takens. Detecting strange attractors in turbulence, Lecture Notes in Mathematics. Vol. 898, Springer-Verlag, Berlin, 1980, pp. 366-381; and in Dynamical System in Turbulence, Warlock, 1980, eds. D. Rand and L.S. Young.

Downloads

Published

2014-08-01

How to Cite

Golovko, V. (2014). ESTIMATION OF THE LYAPUNOV SPECTRUM FROM ONE-DIMENSIONAL OBSERVATIONS USING NEURAL NETWORKS. International Journal of Computing, 2(2), 30-34. https://doi.org/10.47839/ijc.2.2.201

Issue

2003, Volume 2, Issue 2

Section

Articles

License

International Journal of Computing is an open access journal. Authors who publish with this journal agree to the following terms:
•    Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
•    Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
•    Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work.