COMPUTING OF LYAPUNOV EXPONENTS TECHNIQUES USING NEURAL NETWORKS

Authors

  • Vladimir Golovko
  • Yury Savitsky

DOI:

https://doi.org/10.47839/ijc.3.1.258

Keywords:

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

Abstract

The authors examine neural network techniques for computing of Lyapunov spectrum using observations from unknown dynamical system. Such an approach is based on 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 scalar time series. The results of experiments are discussed.

References

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

Holger Kantz, Tomas Schreiber. Nonlinear time series analysis. Cambridge, Cambridge University Press, 1997.

Proceedings of the 1999 Workshop ''Chaos in Brain?". World Scientific, Singapore, 2000.

L. D. Iasemides, J. C. Sackellares. Chaos theory and epilepsy. The Neuroscientist, 2 (1996), pp. 118-126.

D. Kugiumtzis, P. G. Larsson. "Linear and Nonlinear Analysis of EEG for the Prediction of Epileptic Seizures", Proceedings of the 1999 Workshop ''Chaos in Brain?'', World Scientific, Singapore, pp. 329 - 333, 2000.

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. - 25p.

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.

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Published

2014-08-01

How to Cite

Golovko, V., & Savitsky, Y. (2014). COMPUTING OF LYAPUNOV EXPONENTS TECHNIQUES USING NEURAL NETWORKS. International Journal of Computing, 3(1), 93-98. https://doi.org/10.47839/ijc.3.1.258

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Articles