Copyright © 2012 Changjin Xu and Peiluan 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. H. Jiang and J. Cao, “BAM-type Cohen-Grossberg neural networks with time delays,” Mathematical and Computer Modelling, vol. 47, no. 1-2, pp. 92–103, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
2. C. Huang, L. Huang, and Z. Yuan, “Global stability analysis of a class of delayed cellular neural networks,” Mathematics and Computers in Simulation, vol. 70, no. 3, pp. 133–148, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
3. S. Guo and L. Huang, “Hopf bifurcating periodic orbits in a ring of neurons with delays,” Physica D, vol. 183, no. 1-2, pp. 19–44, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
4. X.-P. Yan, “Hopf bifurcation and stability for a delayed tri-neuron network model,” Journal of Computational and Applied Mathematics, vol. 196, no. 2, pp. 579–595, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
5. A. Hajihosseini, G. R. Rokni 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 · View at Scopus
6. X. Liao, S. Li, and G. Chen, “Bifurcation analysis on a two-neuron system with distributed delays in the frequency domain,” Neural Networks, vol. 17, no. 4, pp. 545–561, 2004. View at Publisher · View at Google Scholar · View at Scopus
7. G. Agranovich, E. Litsyn, and A. Slavova, “Impulsive control of a hysteresis cellular neural network model,” Nonlinear Analysis, vol. 3, no. 1, pp. 65–73, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
8. S. Guo, X. Tang, and L. Huang, “Stability and bifurcation in a discrete system of two neurons with delays,” Nonlinear Analysis, vol. 9, no. 4, pp. 1323–1335, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
9. S. Guo, “Equivariant Hopf bifurcation for functional differential equations of mixed type,” Applied Mathematics Letters, vol. 24, no. 5, pp. 724–730, 2011. View at Publisher · View at Google Scholar
10. J. Wei and C. Zhang, “Bifurcation analysis of a class of neural networks with delays,” Nonlinear Analysis, vol. 9, no. 5, pp. 2234–2252, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
11. J. Wei and M. Y. Li, “Global existence of periodic solutions in a tri-neuron network model with delays,” Physica D, vol. 198, no. 1-2, pp. 106–119, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
12. S. Li, X. Liao, C. Li, and K.-W. Wong, “Hopf bifurcation of a two-neuron network with different discrete time delays,” International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, vol. 15, no. 5, pp. 1589–1601, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
13. W. Yu and J. Cao, “Stability and Hopf bifurcation on a two-neuron system with time delay in the frequency domain,” International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, vol. 17, no. 4, pp. 1355–1366, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
14. 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
15. C. Zhang, B. Zheng, and L. Wang, “Multiple Hopf bifurcations of symmetric BAM neural network model with delay,” Applied Mathematics Letters, vol. 22, no. 4, pp. 616–622, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
16. H. Zhao and L. Wang, “Hopf bifurcation in Cohen-Grossberg neural network with distributed delays,” Nonlinear Analysis, vol. 8, no. 1, pp. 73–89, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
17. C. Xu, X. Tang, and M. Liao, “Frequency domain analysis for bifurcation in a simplified tri-neuron BAM network model with two delays,” Neural Networks, vol. 23, no. 7, pp. 872–880, 2010. View at Publisher · View at Google Scholar · View at Scopus
18. C. Xu, X. Tang, and M. Liao, “Stability and bifurcation analysis of a six-neuron BAM neural network model with discrete delays,” Neurocomputing, vol. 74, no. 5, pp. 689–707, 2011. View at Publisher · View at Google Scholar · View at Scopus
19. 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 · View at Scopus
20. P. D. Gupta, N. C. Majee, and A. B. Roy, “Stability, bifurcation and global existence of a Hopf-bifurcating periodic solution for a class of three-neuron delayed network models,” Nonlinear Analysis, vol. 67, no. 10, pp. 2934–2954, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
21. R. Curtu, “Singular Hopf bifurcations and mixed-mode oscillations in a two-cell inhibitory neural network,” Physica D, vol. 239, no. 9, pp. 504–514, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
22. H. Zhao, L. Wang, and C. Ma, “Hopf bifurcation and stability analysis on discrete-time Hopfield neural network with delay,” Nonlinear Analysis, vol. 9, no. 1, pp. 103–113, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
23. H. Hu and L. Huang, “Stability and Hopf bifurcation analysis on a ring of four neurons with delays,” Applied Mathematics and Computation, vol. 213, no. 2, pp. 587–599, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
24. 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
25. K. L. Babcock and R. M. Westervelt, “Dynamics of simple electronic neural networks,” Physica D, vol. 28, no. 3, pp. 305–316, 1987. View at Publisher · View at Google Scholar
26. K. L. Babcock and R. M. Westervelt, “Dynamics of simple electronic neural networks,” Physica D, vol. 28, no. 3, pp. 305–316, 1987. View at Publisher · View at Google Scholar
27. Y. Lin, J. Li, and J. Cao, “The Hopf bifurcation direction of a four-dimensional electronic neural network system,” Systems Science and Mathematical Sciences, vol. 10, no. 4, pp. 337–343, 1997.
28. 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 Zentralblatt MATH
29. Y. Kuang, Delay Differential Equations with Applications in Population Dynamics, vol. 191 of Mathematics in Science and Engineering, Academic Press, Boston, Mass, USA, 1993.
30. J. Hale, Theory of Functional Differential Equations, vol. 3, Springer, New York, NY, USA, 2nd edition, 1977.
31. 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, UK, 1981.