Table of Contents
ISRN Applied Mathematics
Volume 2011, Article ID 636732, 6 pages
http://dx.doi.org/10.5402/2011/636732
Research Article

Hopf Bifurcation Analysis in a Tabu Learning Neuron Model with Two Delays

School of Mathematics and Computer Science, Fujian Normal University, Fuzhou, Fujian 350007, China

Received 10 March 2011; Accepted 29 March 2011

Academic Editors: C.-C. Chiu and A. El-Sayed

Copyright © 2011 Yingguo Li. 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. J. J. Hopfield, “Neurons with graded response have collective computational properties like those of two-state neurons,” Proceedings of the National Academy of Sciences of the United States of America, vol. 81, no. 10, pp. 3088–3092, 1984. View at Google Scholar · View at Scopus
  2. D. A. Beyer and R. G. Ogier, “Tabu learning: a neural network search method for solving nonconvexoptimization problems,” in Proceedings of the International Joint Conference on Neural Networks (IJCNN '91), pp. 953–961, Singapore, July 1991.
  3. C. Li, X. Liao, and J. Yu, “Tabu learning method for multiuser detection in CDMA systems,” Neurocomputing, vol. 49, pp. 411–415, 2002. View at Publisher · View at Google Scholar · View at Scopus
  4. F. Glover, “Tabu search, part I,” ORSA Journal on Computing, vol. 1, pp. 190–206, 1989. View at Google Scholar
  5. F. Glover, “Tabu search, part II,” ORSA Journal on Computing, vol. 2, pp. 4–32, 1990. View at Google Scholar
  6. C. Li, H. Xu, X. Liao, and J. Yu, “Tabu search for CNN template learning,” Neurocomputing, vol. 51, pp. 475–479, 2003. View at Publisher · View at Google Scholar · View at Scopus
  7. C. Li, X. Liao, and J. Yu, “Tabu search for fuzzy optimization and applications,” Information Sciences, vol. 158, no. 1–4, pp. 3–13, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. C. Li, G. Chen, X. Liao, and J. Yu, “Hopf bifurcation and chaos in tabu learning neuron models,” International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, vol. 15, no. 8, pp. 2633–2642, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. M. Xiao and J. Cao, “Bifurcation analysis on a discrete-time tabu learning model,” Journal of Computational and Applied Mathematics, vol. 220, no. 1-2, pp. 725–738, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  10. C. Huang, Y. He, L. Huang, and Y. Zhaohui, “Hopf bifurcation analysis of two neurons with three delays,” Nonlinear Analysis: Real World Applications, vol. 8, no. 3, pp. 903–921, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  11. C. Huang, L. Huang, J. Feng, M. Nai, and Y. He, “Hopf bifurcation analysis for a two-neuron network with four delays,” Chaos, Solitons and Fractals, vol. 34, no. 3, pp. 795–812, 2007. View at Publisher · View at Google Scholar · View at MathSciNet
  12. D. A. Beyer and R. G. Ogier, “Tabu learning: a neural network search method for solving nonconvex optimization problems,” in Proceedings of the International Joint Conference on Neural Networks (IJCNN '91), pp. 953–961, Singapore, July 1991.
  13. K. Gopalsamy and I. Leung, “Delay induced periodicity in a neural netlet of excitation and inhibition,” Physica D, vol. 89, no. 3-4, pp. 395–426, 1996. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  14. L. Olien and J. Bélair, “Bifurcations, stability, and monotonicity properties of a delayed neural network model,” Physica D, vol. 102, no. 3-4, pp. 349–363, 1997. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  15. J. Wei and S. Ruan, “Stability and bifurcation in a neural network model with two delays,” Physica D, vol. 130, no. 3-4, pp. 255–272, 1999. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  16. K. L. Cooke and Z. Grossman, “Discrete delay, distributed delay and stability switches,” Journal of Mathematical Analysis and Applications, vol. 86, no. 2, pp. 592–627, 1982. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  17. S. Ruan, “Absolute stability, conditional stability and bifurcation in Kolmogorov-type predator-prey systems with discrete delays,” Quarterly of Applied Mathematics, vol. 59, no. 1, pp. 159–173, 2001. View at Google Scholar · View at Zentralblatt MATH