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Discrete Dynamics in Nature and Society
Volume 2013 (2013), Article ID 683091, 7 pages
Almost Periodic Solutions for Wilson-Cowan Type Model with Time-Varying Delays
School of Science, Jimei University, Xiamen 361021, China
Received 9 October 2012; Accepted 26 December 2012
Academic Editor: Junli Liu
Copyright © 2013 Shasha Xie and Zhenkun Huang. 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.
- H. R. Wilson and J. D. Cowan, “Excitatory and inhibitory interactions in localized populations of model neurons,” Biophysical Journal, vol. 12, no. 1, pp. 1–24, 1972.
- H. R. Wilson and J. D. Cowan, “A mathematical theory of the functional dynamics of cortical and thalamic nervous tissue,” Kybernetik, vol. 13, no. 2, pp. 55–80, 1973.
- C. van Vreeswijk and H. Sompolinsky, “Chaos in neuronal networks with balanced excitatory and inhibitory activity,” Science, vol. 274, no. 5293, pp. 1724–1726, 1996.
- S. E. Folias and G. B. Ermentrout, “New patterns of activity in a pair of interacting excitatory-inhibitory neural fields,” Physical Review Letters, vol. 107, no. 22, Article ID 228103, 2011.
- K. Mantere, J. Parkkinen, T. Jaaskelainen, and M. M. Gupta, “Wilson-Cowan neural-network model in image processing,” Journal of Mathematical Imaging and Vision, vol. 2, no. 2-3, pp. 251–259, 1992.
- L. H. A. Monteiro, M. A. Bussab, and J. G. C. Berlinck, “Analytical results on a Wilson-Cowan neuronal network modified model,” Journal of Theoretical Biology, vol. 219, no. 1, pp. 83–91, 2002.
- B. Pollina, D. Benardete, and V. W. Noonburg, “A periodically forced Wilson-Cowan system,” SIAM Journal on Applied Mathematics, vol. 63, no. 5, pp. 1585–1603, 2003.
- R. Decker and V. W. Noonburg, “A periodically forced Wilson-Cowan system with multiple attractors,” SIAM Journal on Mathematical Analysis, vol. 44, no. 2, pp. 887–905, 2012.
- P. L. William, “Equilibrium and stability of wilson and cowan's time coarse graining model,” in Proceedings of the 20th International Symposium on Mathematical Theory of Networks and Systems (MTNS '12), Melbourne, Australia, July 2012.
- Z. Huang, S. Mohamad, X. Wang, and C. Feng, “Convergence analysis of general neural networks under almost periodic stimuli,” International Journal of Circuit Theory and Applications, vol. 37, no. 6, pp. 723–750, 2009.
- Y. Liu and Z. You, “Multi-stability and almost periodic solutions of a class of recurrent neural networks,” Chaos, Solitons and Fractals, vol. 33, no. 2, pp. 554–563, 2007.
- C. Y. He, Almost Periodic Differential Equation, Higher Education, Beijing, China, 1992.
- H. Zhenkun, F. Chunhua, and S. Mohamad, “Multistability analysis for a general class of delayed Cohen-Grossberg neural networks,” Information Sciences, vol. 187, pp. 233–244, 2012.
- H. Zhenkun and Y. N. Raffoul, “Biperiodicity in neutral-type delayed difference neural networks,” Advances in Difference Equations, vol. 2012, article 5, 2012.