Analysis of Equilibria of a Recurrent Neural Network involving Transcendental Function
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
@article{key:article, 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" }
Abstract
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.
Reference
- 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.
- 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.
- D. Marr. and T. Poggio. Cooperative computation of stereo disparity, sci. , vol 194 pp 283 –287, 1976.
- J. K. Hale, Theory of function differential equations 2nd ed. Applied mathematical sciences, vol. 3 Springer , new York, 1977.
- 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.
- 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 .
- 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.
- R. Szeliski. "cooperative algorithms for solving random dot stereo grams" , Carnegie Mellon Univ. Tech Rep CMU-CS –86-133,1986.
- 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
- 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.
Keywords
Neural network, limit cycle, nonlinear dynamics, learning systems, transcendental function, equilibrium