Table of Contents Author Guidelines Submit a Manuscript
Discrete Dynamics in Nature and Society
Volume 2014, Article ID 971520, 8 pages
http://dx.doi.org/10.1155/2014/971520
Research Article

Equivariant Bifurcation in Coupled Two Neural Network Rings

Department of Mathematics, Harbin Institute of Technology, Harbin 150001, China

Received 6 November 2014; Accepted 1 December 2014; Published 30 December 2014

Academic Editor: Victor S. Kozyakin

Copyright © 2014 Baodong Zheng and Haidong Yin. 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. A. P. S. Dias and J. S. W. Lamb, “Local bifurcation in symmetric coupled cell networks: linear theory,” Physica D: Nonlinear Phenomena, vol. 223, no. 1, pp. 93–108, 2006. View at Publisher · View at Google Scholar · View at Scopus
  2. P. Perlikowski, S. Yanchuk, O. V. Popovych, and P. A. Tass, “Periodic patterns in a ring of delay-coupled oscillators,” Physical Review E: Statistical, Nonlinear, and Soft Matter Physics, vol. 82, no. 3, Article ID 036208, 2010. View at Publisher · View at Google Scholar · View at Scopus
  3. M. Bonnin, “Waves and patterns in ring lattices with delays,” Physica D: Nonlinear Phenomena, vol. 238, no. 1, pp. 77–87, 2009. View at Publisher · View at Google Scholar · View at Scopus
  4. P. Zhang, S. Guo, and Y. He, “Dynamics of a delayed two-coupled oscillator with excitatory-to-excitatory connection,” Applied Mathematics and Computation, vol. 216, no. 2, pp. 631–646, 2010. View at Publisher · View at Google Scholar · View at Scopus
  5. C. Zhang, B. Zheng, and L. Wang, “Multiple Hopf bifurcations of three coupled van der Pol oscillators with delay,” Applied Mathematics and Computation, vol. 217, no. 17, pp. 7155–7166, 2011. View at Publisher · View at Google Scholar · View at Scopus
  6. F. Drubi, S. Ibáñez, and J. Á. Rodríguez, “Coupling leads to chaos,” Journal of Differential Equations, vol. 239, no. 2, pp. 371–385, 2007. View at Publisher · View at Google Scholar · View at Scopus
  7. M. Golubitsky, I. N. Stewart, and D. G. Schaeffer, Singularities and Groups in Bifurcation Theory: Vol. 7, vol. 69 of Applied Mathematical Sciences, Springer, New York, NY, USA, 1988.
  8. A. K. Yuri, Elements of Applied Bifurcation Theory, Springer, New York, NY, USA, 1995.
  9. S. Guo and J. Man, “Patterns in hierarchical networks of neuronal oscillators with D3 × Z3 symmetry,” Journal of Differential Equations, vol. 254, no. 8, pp. 3501–3529, 2013. View at Publisher · View at Google Scholar · View at Scopus
  10. S. A. Campbell, R. Edwards, and P. van den Driessche, “Delayed coupling between two neural network loops,” SIAM Journal on Applied Mathematics, vol. 65, no. 1, pp. 316–335, 2005. View at Publisher · View at Google Scholar · View at Scopus
  11. C. Zhang, Y. Zhang, and B. Zheng, “A model in a coupled system of simple neural oscillators with delays,” Journal of Computational and Applied Mathematics, vol. 229, no. 1, pp. 264–273, 2009. View at Publisher · View at Google Scholar · View at Scopus