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Abstract and Applied Analysis
Volume 2011, Article ID 697630, 21 pages
http://dx.doi.org/10.1155/2011/697630
Research Article

Stability and Bifurcation Analysis in a Class of Two-Neuron Networks with Resonant Bilinear Terms

1Guizhou Key Laboratory of Economics System Simulation, Guizhou College of Finance and Economics, Guiyang 550004, China
2Department of Mathematics, Zhangjiajie College of jishou University, Zhangjiajie 427000, China

Received 8 January 2011; Revised 27 February 2011; Accepted 27 April 2011

Academic Editor: Nobuyuki Kenmochi

Copyright © 2011 Changjin Xu and Xiaofei He. 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, “Neural networks and physical systems with emergent collective computational abilities,” Proceedings of the National Academy of Sciences of the United States of America, vol. 79, no. 8, pp. 2554–2558, 1982. View at Publisher · View at Google Scholar
  2. 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 I, pp. 3088–3092, 1984. View at Publisher · View at Google Scholar
  3. S. Guo, L. Huang, and L. Wang, “Linear stability and Hopf bifurcation in a two-neuron network with three delays,” International Journal of Bifurcation and Chaos, vol. 14, no. 8, pp. 2799–2810, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  4. X. Liao, K.-W. Wong, and Z. Wu, “Bifurcation analysis on a two-neuron system with distributed delays,” Physica D, vol. 149, no. 1-2, pp. 123–141, 2001. View at Publisher · View at Google Scholar
  5. 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
  6. 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
  7. B. Wang and J. Jian, “Stability and Hopf bifurcation analysis on a four-neuron BAM neural network with distributed delays,” Communications in Nonlinear Science and Numerical Simulation, vol. 15, no. 2, pp. 189–204, 2010. View at Publisher · View at Google Scholar
  8. Z. Yuan, D. Hu, and L. Huang, “Stability and bifurcation analysis on a discrete-time neural network,” Journal of Computational and Applied Mathematics, vol. 177, no. 1, pp. 89–100, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  9. A. Hajihosseini, G. R. R. Lamooki, B. Beheshti, and F. Maleki, “The Hopf bifurcation analysis on a time-delayed recurrent neural network in the frequency domain,” Neurocomputing, vol. 73, no. 4-6, pp. 991–1005, 2010. View at Publisher · View at Google Scholar
  10. S. Guo and Y. Yuan, “Delay-induced primary rhythmic behavior in a two-layer neural network,” Neural Networks, vol. 24, no. 1, pp. 65–74, 2011. View at Publisher · View at Google Scholar
  11. Y. Song, M. Han, and J. Wei, “Stability and Hopf bifurcation analysis on a simplified BAM neural network with delays,” Physica D, vol. 200, no. 3-4, pp. 185–204, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  12. J. Wei and C. Zhang, “Bifurcation analysis of a class of neural networks with delays,” Nonlinear Analysis. Real World Applications. An International Multidisciplinary Journal, vol. 9, no. 5, pp. 2234–2252, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  13. W. Yu and J. Cao, “Stability and Hopf bifurcation analysis on a four-neuron BAM neural network with time delays,” Physics Letters, Section A, vol. 351, no. 1-2, pp. 64–78, 2006. View at Publisher · View at Google Scholar
  14. X. Yang, M. Yang, H. Liu, and X. Liao, “Bautin bifurcation in a class of two-neuron networks with resonant bilinear terms,” Chaos, Solitons and Fractals, vol. 38, no. 2, pp. 575–589, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  15. S. Ruan and J. Wei, “On the zeros of transcendental functions with applications to stability of delay differential equations with two delays,” Dynamics of Continuous, Discrete & Impulsive Systems. Series A., vol. 10, no. 6, pp. 863–874, 2003. View at Google Scholar · View at Zentralblatt MATH
  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. B. D. Hassard, N. D. Kazarinoff, and Y. H. Wan, Theory and applications of Hopf bifurcation, vol. 41 of London Mathematical Society Lecture Note Series, Cambridge University Press, Cambridge, 1981.