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Analysis of Equilibria of a Recurrent Neural Network involving Transcendental Function

Neeraj Sahu, A. K. Verma Published in Artificial Intelligence

International Journal of Applied Information Systems
Year of Publication 2012
© 2010 by IJAIS Journal
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  1. Neeraj Sahu and A K Verma. Article: Analysis of Equilibria of a Recurrent Neural Network involving Transcendental Function. International Journal of Applied Information Systems 4(5):6-12, October 2012. BibTeX

    	author = "Neeraj Sahu and A. K. Verma",
    	title = "Article: Analysis of Equilibria of a Recurrent Neural Network involving Transcendental Function",
    	journal = "International Journal of Applied Information Systems",
    	year = 2012,
    	volume = 4,
    	number = 5,
    	pages = "6-12",
    	month = "October",
    	note = "Published by Foundation of Computer Science, New York, USA"


In this paper we present four node recurrent neural networks system with three weight parameters. This closed recurrent neural network generates a limit cycle. In this system for which the equation of equilibria involves transcendental function tan h(X) and its iterates. The network is shown to trains a desired periodic signal by varying weights.


  1. A. Ruiz, D. H. Owens, and S. Townley, "Existence, learning, and replication of periodic motions in recurrent neural network," IEEE Trans. Neural Network. Vol. 9. no 4, pp 651- 661, jul. 1998.
  2. Bo. Gao, and Weinian. Zhang, "Equilibria and their bifurcation in a recurrent neural network involving iterates of a transcendental function," IEEE Trans. Neural Networks. Vol. 19 No. 5. Pp. 782-794, May 2008.
  3. D. Marr. and T. Poggio. Cooperative computation of stereo disparity, sci. , vol 194 pp 283 –287, 1976.
  4. J. K. Hale, Theory of function differential equations 2nd ed. Applied mathematical sciences, vol. 3 Springer , new York, 1977.
  5. J. J. Hofield, Neurons with graded response have collective computational properties like those of two state neurons proceeding of the national academy of sciences of the United States of America 81 (1984) no . 10 3088- 3092.
  6. J. L. McClelland. D. E. Rumclhart. and G. E. Hinton. "The appeal of parallel distributed processing. " in Rinehart. D. E. , McClelland. J. L. , and the PDP research group Eds. , parallel distributed processing explorations in microstructure of cognition volume l. Foundations Cambridge MA:MIT Press 1986 .
  7. S. Hasting, J. Tyson, and D. Webster, "Existence of periodic solution for negative feedback cellular control system," J. Differential Equations, vol. 25, pp. 39-64,1977.
  8. R. Szeliski. "cooperative algorithms for solving random dot stereo grams" , Carnegie Mellon Univ. Tech Rep CMU-CS –86-133,1986.
  9. Yingguo Li "Stability and Bifurcation Analysis of a Three- Dimensional Recurrent Neural Network with Time Delay" Hindawi Publishing Corporation Journal of Applied Mathematics. Volume 2012 Article ID 357382, 13 pages doi:10. 1155/2012/357382
  10. Yujiao Huang, Huaguang Zhang, Zhanshan Wang and Mo Zhao. "Stability Analysis of Multiple Equilibria for Recurrent Neural Networks," Advances in neural network-ISNN 2012. Lecture notes in computer science Volume 7367, 2012, pp196-205.


Neural network, limit cycle, nonlinear dynamics, learning systems, transcendental function, equilibrium