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Abstract and Applied Analysis
Volume 2012 (2012), Article ID 109319, 14 pages
Global Convergence for Cohen-Grossberg Neural Networks with Discontinuous Activation Functions
1School of Mathematics and Physics, Anhui University of Technology, Ma'anshan 243002, China
2School of Computer Science, Anhui University of Technology, Ma'anshan 243002, China
Received 12 September 2012; Accepted 23 October 2012
Academic Editor: Sabri Arik
Copyright © 2012 Yanyan Wang and Jianping Zhou. 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.
- M. A. Cohen and S. Grossberg, “Absolute stability of global pattern formation and parallel memory storage by competitive neural networks,” IIEEE Transactions on Systems, Man, and Cybernetics, vol. 13, no. 5, pp. 815–826, 1983.
- K. Gopalsamy, “Global asymptotic stability in a periodic Lotka-Volterra system,” Australian Mathematical Society B, vol. 27, no. 1, pp. 66–72, 1985.
- X. Liao, S. Yang, S. Chen, and Y. Fu, “Stability of general neural networks with reaction-diffusion,” Science in China F, vol. 44, pp. 389–395, 2001.
- W. Lu and T. Chen, “New conditions on global stability of Cohen-Grossberg neural networks,” Neural Computation, vol. 15, no. 5, pp. 1173–1189, 2003.
- K. Yuan and J. Cao, “An analysis of global asymptotic stability of delayed Cohen-Grossberg neural networks via nonsmooth analysis,” IEEE Transactions on Circuits and Systems I, vol. 52, no. 9, pp. 1854–1861, 2005.
- J. Cao and X. Li, “Stability in delayed Cohen-Grossberg neural networks: LMI optimization approach,” Physica D, vol. 212, no. 1-2, pp. 54–65, 2005.
- C. C. Hwang, C. J. Cheng, and T. L. Liao, “Globally exponential stability of generalized Cohen-Grossberg neural networks with delays,” Physics Letters A, vol. 319, no. 1-2, pp. 157–166, 2003.
- J. Cao and J. Liang, “Boundedness and stability for Cohen-Grossberg neural network with time-varying delays,” Journal of Mathematical Analysis and Applications, vol. 296, no. 2, pp. 665–685, 2004.
- J. Zhang, Y. Suda, and H. Komine, “Global exponential stability of Cohen-Grossberg neural networks with variable delays,” Physics Letters A, vol. 338, no. 1, pp. 44–50, 2005.
- T. Chen and L. Rong, “Robust global exponential stability of Cohen-Grossberg neural networks with time delays,” IEEE Transactions on Neural Networks, vol. 15, no. 1, pp. 203–205, 2004.
- M. Forti and P. Nistri, “Global convergence of neural networks with discontinuous neuron activations,” IEEE Transactions on Circuits and Systems I, vol. 50, no. 11, pp. 1421–1435, 2003.
- H. Harrer, J. A. Nossek, and R. Stelzl, “An analog implementation of discrete-time cellular neural networks,” IEEE Transactions on Neural Networks, vol. 3, no. 3, pp. 466–476, 1992.
- M. P. Kennedy and L. O. Chua, “Neural networks for nonlinear programming,” IEEE Transactions on Circuits and Systems I, vol. 35, no. 5, pp. 554–562, 1988.
- L. O. Chua, C. A. Desoer, and E. S. Kuh, Linear and Nonlinear Circuits, McGraw-Hill, New York, NY, USA, 1987.
- V. I. Utkin, Sliding Modes and Their Application in Variable Structure Systems, U.S.S.R.: MIR, Moscow, Russia, 1978.
- J.-P. Aubin and A. Cellina, Differential Inclusions, Springer, Berlin, Germany, 1984.
- B. E. Paden and S. S. Sastry, “A calculus for computing Filippov's differential inclusion with application to the variable structure control of robot manipulators,” IEEE Transactions on Circuits and Systems, vol. 34, no. 1, pp. 73–82, 1987.
- M. Forti, “M-matrices and global convergence of discontinuous neural networks,” International Journal of Circuit Theory and Applications, vol. 35, no. 2, pp. 105–130, 2007.
- W. Lu and T. Chen, “Dynamical behaviors of delayed neural network systems with discontinuous activation functions,” Neural Computation, vol. 18, no. 3, pp. 683–708, 2006.
- W. Lu and T. Chen, “Dynamical behaviors of Cohen-Grossberg neural networks with discontinuous activation functions,” Neural Networks, vol. 18, no. 3, pp. 231–242, 2005.
- A. F. Filippov, “Differential equations with discontinuous right-hand side,” Transactions of the American Mathematical Society, vol. 42, pp. 199–231, 1964.
- M. Hirsch, “Convergent activation dynamics in continuous time networks,” Neural Networks, vol. 2, pp. 331–349, 1989.
- D. Hershkowitz, “Recent directions in matrix stability,” Linear Algebra and its Applications, vol. 171, pp. 161–186, 1992.
- H. Wu, “Global stability analysis of a general class of discontinuous neural networks with linear growth activation functions,” Information Sciences, vol. 179, no. 19, pp. 3432–3441, 2009.
- G. Huang and J. Cao, “Multistability of neural networks with discontinuous activation function,” Communications in Nonlinear Science and Numerical Simulation, vol. 13, no. 10, pp. 2279–2289, 2008.
- H. Wu and C. Shan, “Stability analysis for periodic solution of BAM neural networks with discontinuous neuron activations and impulses,” Applied Mathematical Modelling, vol. 33, no. 6, pp. 2564–2574, 2009.
- C. Huang and J. Cao, “Stochastic dynamics of nonautonomous Cohen-Grossberg neural networks,” Abstract and Applied Analysis, vol. 2011, Article ID 297147, 17 pages, 2011.
- X. Yang, C. Huang, D. Zhang, and Y. Long, “Dynamics of Cohen-Grossberg neural networks with mixed delays and impulses,” Abstract and Applied Analysis, vol. 2008, Article ID 432341, 14 pages, 2008.
- Q. Liu and W. Zheng, “Bifurcation of a Cohen-Grossberg neural network with discrete delays,” Abstract and Applied Analysis, vol. 2012, Article ID 909385, 11 pages, 2012.
- M. J. Park, O. M. Kwon, J. H. Park, S. M. Lee, and E. J. Cha, “Synchronization criteria for coupled stochastic neural networks with time-varying delays and leakage delay,” Journal of the Franklin Institute, vol. 349, no. 5, pp. 1699–1720, 2012.
- O. M. Kwon, S. M. Lee, J. H. Park, and E. J. Cha, “New approaches on stability criteria for neural networks with interval time-varying delays,” Applied Mathematics and Computation, vol. 218, no. 19, pp. 9953–9964, 2012.
- O. M. Kwon, J. H. Park, S. M. Lee, and E. J. Cha, “A new augmented Lyapunov-Krasovskii functional approach to exponential passivity for neural networks with time-varying delays,” Applied Mathematics and Computation, vol. 217, no. 24, pp. 10231–10238, 2011.