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Discrete Dynamics in Nature and Society
Volume 2013 (2013), Article ID 143706, 8 pages
Existence of Periodic Solutions for Shunting Inhibitory Cellular Neural Networks with Neutral Delays
Fujian Preschool Education College, Fuzhou, Fujian 350007, China
Received 3 July 2013; Accepted 16 September 2013
Academic Editor: Cecile Piret
Copyright © 2013 Ninghua Chen. 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.
- A. Bouzerdoum and R. B. Pinter, “Shunting inhibitory cellular neural networks: derivation and stability analysis,” IEEE Transactions on Circuits and Systems I, vol. 40, no. 3, pp. 215–221, 1993.
- A. Bouzerdoum and R. B. Pinter, “Analysis and analog implementation of directionally sensitive shunting inhibitory cellular neural networks,” in Visual Information Processing: From Neurons to Chips, vol. 1473 of Proceedings of SPIE, pp. 29–38, 1991.
- Y. K. Li, C. Liu, and L. Zhu, “Global exponential stability of periodic solution of shunting inhibitory CNNs with delays,” Physics Letters A, vol. 337, pp. 46–54, 2005.
- Y. Xia, J. Cao, and Z. Huang, “Existence and exponential stability of almost periodic solution for shunting inhibitory cellular neural networks with impulses,” Chaos, Solitons & Fractals, vol. 34, no. 5, pp. 1599–1607, 2007.
- K. Gopalsamy, Stability and Oscillations in Delay Differential Equations of Population Dynamics, vol. 74, Kluwer Academic, Boston, Mass, USA, 1992.
- J. Hale and S. M. Verduyn Lunel, Introduction To Functional Differential Equations, Springer, New York, NY, USA, 1993.
- J. H. Park, O. M. Kwon, and S. M. Lee, “State estimation for neural networks of neutral-type with interval time-varying delays,” Applied Mathematics and Computation, vol. 203, no. 1, pp. 217–223, 2008.
- J. H. Park, O. M. Kwon, and S. M. Lee, “LMI optimization approach on stability for delayed neural networks of neutral-type,” Applied Mathematics and Computation, vol. 196, no. 1, pp. 236–244, 2008.
- J. H. Park, C. H. Park, O. M. Kwon, and S. M. Lee, “A new stability criterion for bidirectional associative memory neural networks of neutral-type,” Applied Mathematics and Computation, vol. 199, no. 2, pp. 716–722, 2008.
- S. M. Lee, O. M. Kwon, and J. H. Park, “A novel delay-dependent criterion for delayed neural networks of neutral type,” Physics Letters A, vol. 374, no. 17-18, pp. 1843–1848, 2010.
- S. Mandal and N. C. Majee, “Existence of periodic solutions for a class of Cohen-Grossberg type neural networks with neutral delays,” Neurocomputing, vol. 74, pp. 1000–1007, 2011.
- K. Wang and Y. Zhu, “Stability of almost periodic solution for a generalized neutral-type neural networks with delays,” Neurocomputing, vol. 73, pp. 3300–3307, 2010.
- Y. Li, L. Zhao, and X. Chen, “Existence of periodic solutions for neutral type cellular neural networks with delays,” Applied Mathematical Modelling, vol. 36, no. 3, pp. 1173–1183, 2012.
- Z. Gui, W. Ge, and X. Yang, “Periodic oscillation for a Hopfield neural networks with neutral delays,” Physics Letters A, vol. 364, pp. 267–273, 2007.
- K. Deimling, Nonlinear Functional Analysis, Springer, Berlin, Germany, 1985.
- W. Petryshynand and Z. Yu, “Existence theorem for periodic solutions of higher order nonlinear periodic boundary value problems,” Nonlinear Analysis, vol. 69, pp. 943–969, 1982.
- Z. Liu and Y. Mao, “Existence theorem for periodic solutions of higher order nonlinear differential equations,” Journal of Mathematical Analysis and Applications, vol. 216, no. 2, pp. 481–490, 1997.
- S. Lu and W. Ge, “Existence of positive periodic solutions for neutral logarithmic population model with multiple delays,” Journal of Computational and Applied Mathematics, vol. 166, no. 2, pp. 371–383, 2004.