Abstract
In this paper, a class of generalized nonautonomous cellular neural networks with time-varying delays are studied. By means of Lyapunov functional method, improved Young inequality a m b n ≤ ma t − n + nb t m (0 ≤ m ≤ 1, m + n = 1,t > 0) and the homeomorphism theory, several sufficient conditions are given guaranteeing the existence, uniqueness and global exponential stability of the equilibrium point. The proposed results generalize and improve previous works. An illustrative example is also given to demonstrate the effectiveness of the proposed results.
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References
Cao, J.: New Results Concerning Exponential Stability and Periodic Solutions of Delayed Cellular Neural Networks. Physics Letters A 307(2-3), 136–147 (2003)
Cao, J., Chen, T.: Globally Exponentially Robust Stability and Periodicity of Delayed Neural Networks. Chaos, Solitons & Fractals 22, 957–963 (2004)
Cao, J., Wang, J.: Global Exponential Stability and Periodicity of Recurrent Neural Networks with Time Delays. IEEE Trans. Circuits Syst. I 52(5), 920–931 (2005)
Zhao, H., Cao, J.: New Conditions for Global Exponential Stability of Cellular Neural Networks with Delays. Neural Networks 18, 1332–1340 (2005)
Huang, C., Huang, L., Yuan, Z.: Global Stability Analysis of A Class of Delayed Cellular Neural Networks. Mathematics and Computers in Simulation 70(3), 133–148 (2005)
Zhang, Q., Wei, X., Xu, J.: On Global Exponential Stability of Delayed Cellular Neural Networks with Time-Varying Delays. Applied Mathematics and Computation 162, 679–686 (2005)
Sun, C., Feng, C.: Exponential Periodicity and Stability of Delayed Neural Networks. Mathematics and Computers in Simulation 66, 469–478 (2004)
Zhang, Q., Wei, X., Xu, J.: Gloabl Exponential Stability for Nonautonomous Cellular Neural Networks with Delays. Physics Letter A 351(3), 153–160 (2006)
Liang, J., Cao, J.: Boundeness and Stability for Recurrent Neural Networks with Variable Coefficients and Time-Varying Delays. Physics Letters A 318, 53–64 (2003)
Jiang, H., Teng, Z.: Some New Results for Recurrent Neural Networks with Varying-Time Coefficients and Delays. Physics Letters A 338, 446–460 (2005)
Forti, M., Tesi, A.: New Conditions for Global Stability of Neural Networks with Application to Linear and Quadratic Programming Problems. IEEE Trans. Circuits Systems I Fund. Theory Appl. 42, 354–366 (1995)
Kuang, J.: Applied Inequalities (in Chinese). Shandong Science and Technology Press, Jinan (2004)
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Nie, X., Cao, J., Xiao, M. (2007). Stability Analysis of Generalized Nonautonomous Cellular Neural Networks with Time-Varying Delays. In: Liu, D., Fei, S., Hou, ZG., Zhang, H., Sun, C. (eds) Advances in Neural Networks – ISNN 2007. ISNN 2007. Lecture Notes in Computer Science, vol 4491. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-72383-7_112
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DOI: https://doi.org/10.1007/978-3-540-72383-7_112
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-72382-0
Online ISBN: 978-3-540-72383-7
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