Abstract
Most matrixes of Discrete Hopfield neural networks(DHNNs) and DHNNs with delay are constant matrixes. However, most weight matrixes of DHNNses are variable in many realistic systems. So, the weight matrix and the threshold vector with time factor are considered, and DHNNs with weight function matrix (DHNNWFM) is described. Moreover, the result that if weight function matrix and threshold function vector respectively converge to a constant matrix and a constant vector that the corresponding DHNNs is stable or the weight matrix function is a symmetric function matrix, then DHNNWFM is stable, is obtained by matrix analysis.
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References
Hopfield, J.J.: Neural networks and physical systems emergent collective computational abilities. Proc. Nat. Acad. Sci. USA 79, 2554–2558 (1982)
Bruck, J., Goodman, J.W.: A generalized convergence theorem for neural networks. IEEE Trans. on Inform Theory 34, 1089–1092 (1988)
Goles, E., Fogelman, F., Pellegrin, D.: Decreasing energy functions as a tool for studying threshold Network. Discrete Applied Mathematics 12, 261–277 (1985)
Xu, Z.B., Kwong, C.P.: Global Convergence and Asymptotic Stability of Asymmetric Hopfield Neural Networks. J. Mathematical Analysis and Applications 191, 405–427 (1995)
Lee, D.L.: New stability conditions for Hopfield neural networks in partial simultaneous update mode. IEEE Trans. on Neural Networks 10, 975–978 (1999)
Xiang, H., Yan, K.M., Wang, B.Y.: Existence and global exponential stability of periodic solution for delayed high-order Hopfield-type neural networks. Physics Letters A 352, 341–349 (2006)
Zhang, Q., Wei, X., Xu, J.: On Global Exponential Stability of Discrete-Time Hopfield Neural Networks with Variable Delays. Discrete Dynamics in Nature and Society. Article ID: 67675, 9p (2007)
Xu, B., Liu, X., Liao, X.: Global asymptotic stability of high-order Hopfield type neural networks with time delays. Comput. Math. Appl. 45(10-11), 1729–1737 (2003)
Kosmatopoulos, E.B., Polycarpou, M.M., Christodoulou, M.A., Ioannou, P.A.: High-order neural network structures for identification of dynamical systems. IEEE Trans. Neural Networks 6(2), 422–431 (1995)
Xiang, H., Yan, K.M., Wang, B.Y.: Existence and global exponential stability of periodic solution for delayed discrete high-order Hopfield-type neural networks. Discrete Dynamics in Nature and Society 3, 281–297 (2005)
Bellman, R.: Introduction to Matrix analysis. The Rand Corporation (1970)
Stoer, J., Bulirsch, R.: Introduction to Numerical analysis. Springer, New York (1980)
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Li, J., Diao, Y., Mao, J., Zhang, Y., Yin, X. (2008). Stability Analysis of Discrete Hopfield Neural Networks with Weight Function Matrix. In: Kang, L., Cai, Z., Yan, X., Liu, Y. (eds) Advances in Computation and Intelligence. ISICA 2008. Lecture Notes in Computer Science, vol 5370. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-92137-0_83
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DOI: https://doi.org/10.1007/978-3-540-92137-0_83
Publisher Name: Springer, Berlin, Heidelberg
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