Abstract
In this paper, we discuss delayed Cohen-Grossberg neural networks with time-varying and distributed delays and investigate their global asymptotical stability of the equilibrium point. The model proposed in this paper is universal. A set of sufficient conditions ensuring global convergence and globally exponential convergence for the Cohen-Grossberg neural networks with time-varying and distributed delays are given. Most of the existing models and global stability results for Cohen-Grossberg neural networks, Hopfield neural networks and cellular neural networks can be obtained from the theorems given in this paper.
Keywords
- Neural Network
- Exponential Stability
- Cellular Neural Network
- Exponential Convergence
- Hopfield Neural Network
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References
Chen, T., Lu, W.: Stability Analysis of Dynamical Neural Networks. In: IEEE Conf. Neural Networks and Signal Processing, Nanjing, China, pp. 14–17 (2003)
Chen, T.: Universal Approach to Study Delayed Dynamical Syatems. In: Wang, L., Chen, K., S. Ong, Y. (eds.) ICNC 2005. LNCS, vol. 3610, pp. 245–253. Springer, Heidelberg (2005)
Lu, W., Chen, T.: On Periodic Dynamical Systems. Chinese Annals of Mathematics 25B(4), 455–462 (2004)
Chen, T., Lu, W., Chen, G.: Dynamical Behaviors of a Large Class of General Delayed Neural Networks. Neural Computation 17, 949–968 (2005)
Chen, T., Rong, L.: Robust Global Exponential Stability of Cohen-Grossberg Neural Networks With Time Delays. IEEE Trans. Neural Networks 15(1), 203–206 (2004)
Chen, Y.: Global Stability of Neural Networks with Distributed Delays. Neural Networks 15, 867–871 (2002)
Cohen, M.A., Grossberg, S.: Absolute Stability and Global Pattern Formation and Parallel Memory Storage by Competitive Neural Networks. IEEE Trans. Syst. Man Cybern. B. (13), 815–821 (1983)
Deng, J., Xu, D., Yang, Z.: Global Exponental Stability Analysis of Cohen-Grossberg Neural Networks with Multiple Time-Varying Delays. In: Proceedings of 11th IEEE International Conference on Electronics, Circuits and Systems, pp. 230–233 (2004)
Hwang, C., Cheng, C., Liao, T.: Globally Exponential Stability of Generalized Cohen-Grossberg Neural Netqorks with Delays. Physics Letters A 319, 157–166 (2003)
Liu, J.: Global Exponential Stability of Cohen-Grossberg Neural Networks with Time-Varying Delays. Chaos, Solitons and Fractals 26, 935–945 (2005)
Lu, H.: Global Exponental Stability Analysis of Cohen-Grossberg Neural Networks. IEEE Trans. on Circuits and Systems II 52(9), 476–479 (2005)
Liao, X., Li, C., Wong, K.: Criteria for Exponential Stability of Cohen-Grossberg Neural Networks. Neural Networks 17, 1401–1414 (2004)
Sun, J., Wan, L.: Global Exponential Stability of Cohen-Grossberg Neural Networks with Continuous Distributed Delays. Physics Letters A 342, 331–340 (2005)
Tu, F., Liao, X.: Harmless Delays for Global Asymptotic Stability of Cohen-Grossberg Neural Networks. Chaos, Solitons and Fractals 26, 927–933 (2005)
Wang, L., Zou, X.: Exponential Stability of Cohen-Grossberg Neural Networks. Neural Networks 15, 415–422 (2002)
Ye, H., Michel, A., Wang, K.: Qualitative Analysis of Cohen-Grossberg Neural Networks with Multiple Delays. Physical Review E 51, 2611–2618 (1995)
Zheng, Y., Chen, T.: Global Exponential Stability of Delayed Periodic Dynamical Systems. Physics Letters A 322(5-6), 344–355 (2004)
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Chen, T., Lu, W. (2006). Global Asymptotical Stability of Cohen-Grossberg Neural Networks with Time-Varying and Distributed Delays. In: Wang, J., Yi, Z., Zurada, J.M., Lu, BL., Yin, H. (eds) Advances in Neural Networks - ISNN 2006. ISNN 2006. Lecture Notes in Computer Science, vol 3971. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11759966_29
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DOI: https://doi.org/10.1007/11759966_29
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-34439-1
Online ISBN: 978-3-540-34440-7
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