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Applied Computational Intelligence and Soft Computing
Volume 2009, Article ID 364532, 21 pages
http://dx.doi.org/10.1155/2009/364532
Research Article

Novel FTLRNN with Gamma Memory for Short-Term and Long-Term Predictions of Chaotic Time Series

1Jawaharlal Darda Institute of Engineering & Technology, Yavatmal 445 001, Maharashtra, India
2Applied Electronics Department, Sant Gadge Baba Amravati University, Amravati 444 602, India

Received 3 November 2008; Revised 26 February 2009; Accepted 26 April 2009

Academic Editor: Junbin Gao

Copyright © 2009 Sanjay L. Badjate and Sanjay V. Dudul. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. B. Townshend, “Nonlinear prediction of speech signals,” in Nonlinear Modeling and Forecasting, M. Casdagli and S. Euban, Eds., pp. 433–453, Addison-Wesley, Reading, Mass, USA, 1992. View at Google Scholar
  2. P. G. Cooper, M. N. Hays, and J. E. Whalen, “Neural networks for propagation modeling,” Atlantic Research Corporation Repot 92-12-002, Electromagnetic Environmental Test facility, Fort Huachuca, Ariz, USA, 1992. View at Google Scholar
  3. S. HayKin, Neural Networks: A Comprehensive Foundation, Pearson Education, Delhi, India, 2nd edition, 2006.
  4. A. S. Weigend and N. A. Greshenfeld, Time Series Prediction: Forecasting the Future and Understanding the Past, vol. 15 of Santa Fe Institute Studies in the Sciences of Complexity, Addison-Wesley, Reading, Mass, USA, 1993.
  5. M. Casdagli, “Nonlinear prediction of chaotic time series,” Physica D, vol. 35, no. 3, pp. 335–356, 1989. View at Publisher · View at Google Scholar
  6. H. Leung and T. Lo, “Chaotic radar signal processing over the sea,” IEEE Journal of Oceanic Engineering, vol. 18, no. 3, pp. 287–295, 1993. View at Publisher · View at Google Scholar
  7. H. Leung, “Applying chaos to radar detection in an ocean environment: an experimental study,” IEEE Journal of Oceanic Engineering, vol. 20, no. 1, pp. 56–64, 1995. View at Publisher · View at Google Scholar
  8. K. M. Short, “Steps toward unmasking secure communications,” International Journal of Bifurcation and Chaos, vol. 4, no. 4, pp. 959–977, 1994. View at Publisher · View at Google Scholar
  9. G. Heidari-Bateni and C. D. McGillen, “A chaotic direct-sequence spread-spectrum communication system,” IEEE Transactions on Communications, vol. 42, no. 234, pp. 1524–1527, 1994. View at Publisher · View at Google Scholar
  10. Y. Fu and H. Leung, “Narrow-band interference cancellation in spread-spectrum communication systems using chaos,” IEEE Transactions on Circuits and Systems I, vol. 48, no. 7, pp. 847–858, 2001. View at Publisher · View at Google Scholar
  11. G. Cybenko, “Approximation by superpositions of a sigmoidal function,” Mathematics of Control, Signals, and Systems, vol. 2, no. 4, pp. 303–314, 1989. View at Publisher · View at Google Scholar
  12. K. Hornik, M. Stinchcombe, and H. White, “Multilayer feedforward networks are universal approximators,” Neural Networks, vol. 2, no. 5, pp. 359–366, 1989. View at Publisher · View at Google Scholar
  13. S. V. Dudul, “Prediction of a Lorenz chaotic attractor using two-layer perceptron neural network,” Applied Soft Computing, vol. 5, no. 4, pp. 333–355, 2005. View at Publisher · View at Google Scholar
  14. S. V. Dudul, “Identification of a liquid saturated steam heat exchanger using focused time lagged recurrent neural network model,” IETE Journal of Research, vol. 53, no. 1, pp. 69–82, 2007. View at Google Scholar
  15. A. R. Barron, “Universal approximation bounds for superpositions of a sigmoidal function,” IEEE Transactions on Information Theory, vol. 39, no. 3, pp. 930–945, 1993. View at Publisher · View at Google Scholar
  16. A. Juditsky, H. Hjalmarson, A. Benveniste et al., “Nonlinear black-box models in system identification: mathematical foundations,” Automatica, vol. 31, no. 12, pp. 1725–1750, 1995. View at Publisher · View at Google Scholar
  17. R. Bakker, J. C. Schouten, C. L. Giles, F. Takens, and C. M. van den Bleek, “Learning chaotic attractors by neural networks,” Neural Computations, vol. 12, no. 10, pp. 2355–2383, 2000. View at Publisher · View at Google Scholar
  18. Z. Zhaocoui and D. Yurong, “Chaotic time series analysis based on radial basis function network,” Chinese Journal of Chongqing University, vol. 22, no. 6, pp. 113–120, 1999. View at Google Scholar
  19. H. Leung, T. Lo, and S. Wang, “Prediction of noisy chaotic time series using an optimal radialbasis function neural network,” IEEE Transactions on Neural Networks, vol. 12, no. 5, pp. 1163–1172, 2001. View at Publisher · View at Google Scholar
  20. G. Deco and M. Schurmann, “Neural learning of chaotic system behavior,” IEICE Transactions Fundamentals, vol. E77-A, no. 11, pp. 1840–1845, 1994. View at Google Scholar
  21. U. Thissen, R. van Brakel, A. P. de Weijer, W. J. Melssen, and L. M. C. Buydens, “Using support vector machines for time series prediction,” Chemometrics and Intelligent Laboratory Systems, vol. 69, no. 1-2, pp. 35–49, 2003. View at Publisher · View at Google Scholar
  22. S. A. Billings and H.-L. Wei, “A new class of wavelet networks for nonlinear system identification,” IEEE Transactions on Neural Networks, vol. 16, no. 4, pp. 862–874, 2005. View at Publisher · View at Google Scholar
  23. M. Han, J. Xi, S. Xu, and F.-L. Yin, “Prediction of chaotic time series based on the recurrent predictor neural network,” IEEE Transactions on Signal Processing, vol. 52, no. 12, pp. 3409–3416, 2004. View at Publisher · View at Google Scholar
  24. A. Gholipour, B. N. Araabi, and C. Lucas, “Predicting chaotic time series using neural and neurofuzzy models: a comparative study,” Neural Processing Letters, vol. 24, no. 3, pp. 217–239, 2006. View at Publisher · View at Google Scholar
  25. H. Inoue, Y. Fukunaga, and H. Narihisa, “Efficient hybrid neural network for chaotic time series prediction,” in Proceedings of the International Conference on Artificial Neural Networks (ICANN '01), vol. 2130 of Lecture Notes in Computer Science, pp. 712–718, Springer, Vienna, Austria, August 2001. View at Publisher · View at Google Scholar
  26. M. Han, M. Fan, and J. Xi, “Study of nonlinear multivariate time series prediction based on neural networks,” in Proceedings of the 2nd International Symposium on Neural Networks (ISNN '05), vol. 3497 of Lecture Notes in Computer Science, pp. 618–623, Chongqing, China, May-June 2005. View at Publisher · View at Google Scholar
  27. S.-Z. Qin, H.-T. Su, and T. J. McAvoy, “Comparison of four neural net learning methods for dynamic system identification,” IEEE Transactions on Neural Networks, vol. 3, no. 1, pp. 122–130, 1992. View at Publisher · View at Google Scholar
  28. K. S. Naraendra and K. Parthasarathy, “Identification and control of dynamic systems using neural networks,” IEEE Transactions on Neural Networks, vol. 1, no. 1, pp. 4–27, 1990. View at Publisher · View at Google Scholar
  29. Demuth and M. Beale, “Neural network tool box for use with MATLAB,” Users Guide, Version 4.0, The MathWorks, Inc., Natick, Mass, USA, 2004, http://www.mathworks.com.
  30. G. F. FranKlin, J. D. Powell, and M. L. WorKman, Digital Control of Dynamics Systems, Addison-Wesley, Reading, Mass, USA, 3rd edition, 1998.
  31. F. M. Ham and I. Kostanic, Principles of Neurocomputing for Science and Engineering, Tata McGraw-Hill, New Delhi, India, 2002.
  32. B. de Vries and J. C. Principe, “The gamma model—a new neural model for temporal processing,” Neural Networks, vol. 5, no. 4, pp. 565–576, 1992. View at Publisher · View at Google Scholar
  33. J. C. Principe and N. R. Euliano, Neural and Adaptive Systems: Fundamental through Simulations, John Wiley & Sons, New York, NY, USA, 2000.
  34. M. C. Mackey and L. Glass, “Oscillation and chaos in physiological control systems,” Science, vol. 197, no. 4300, pp. 287–289, 1977. View at Publisher · View at Google Scholar
  35. H. Nijmeijer and H. Berghuis, “On Lyapunov control of the Duffing equation,” IEEE Transactions on Circuits and Systems I, vol. 42, no. 8, pp. 473–477, 1995. View at Publisher · View at Google Scholar
  36. S. Sello, “Solar cycle forecasting: a nonlinear dynamics approach,” Astronomy and Astrophysics, vol. 377, no. 1, pp. 312–320, 2001. View at Publisher · View at Google Scholar
  37. J. K. Lawrence, A. C. Cadavid, and A. A. Ruzmaikin, “Turbulent and chaotic dynamics underlying solar magnetic variability,” Astrophysical Journal, vol. 455, p. 366, 1995. View at Publisher · View at Google Scholar
  38. Q. Zhang, “A nonlinear prediction of the smoothed monthly sunspot numbers,” Astronomy and Astrophysics, vol. 310, pp. 646–650, 1996. View at Google Scholar
  39. T. Schreiber, “Interdisciplinary application of nonlinear time series methods,” Physical Reports, vol. 308, no. 1, pp. 2–64, 1998. View at Google Scholar
  40. http://sidc.oma.be/index.php3.
  41. U. Hübner, N. B. Abraham, and C. O. Weiss, “Dimensions and entropies of chaotic intensity pulsations in a single-mode far-infrared NH3 laser,” Physical Review A, vol. 40, no. 11, pp. 6354–6365, 1989. View at Publisher · View at Google Scholar
  42. I. V. Turchenko, “Simulation modeling of multi-parameter sensor signal identification using neural networks,” in Proceedings of the 2nd IEEE International Conference on Intelligent Systems (IS '04), vol. 3, pp. 48–53, Varna, Bulgaria, June 2004.
  43. G.-B. Huang, Y.-Q. Chen, and H. A. Babri, “Classification ability of single hidden layer feedforward neural networks,” IEEE Transactions on Neural Networks, vol. 11, no. 3, pp. 799–801, 2000. View at Publisher · View at Google Scholar
  44. K. W. Lee and H. N. Lam, “Optimal sizing of feed-forward neural networks: case studies,” in Proceedings of the 2nd New Zealand Two-Stream International Conference on Artificial Neural Networks and Expert Systems (ANNES '95), pp. 71–82, Dunedin, New Zealand, November 1995.