Abstract
The stability of discrete Hopfield neural networks with delay is mainly studied by the use of the state transition equation and the energy function, and some results on the stability are given. The sufficient conditions for the networks with delay converging towards a limit cycle with length 4 are presented. Also, one condition ensuring the network with delay having neither a stable state nor a limit cycle with length 2 is given. The obtained results here partially extend some existing results on stability of discrete Hopfield neural network with delay and without delay.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Xu, Z., Kwong, C.P.: Global Convergence and Asymptotic Stability of Asymmetrical Hopfield Neural Networks. J. Mathematical Analysis and Applications 191, 405–426 (1995)
Lee, D.: New Stability Conditions for Hopfield Neural Networks in Partial Simultaneous Update Mode. IEEE Trans. Neural Networks 10, 975–978 (1999)
Goles, E.: Antisymmetrical Neural Networks. Discrete Applied Mathematics 13, 97–100 (1986)
Ma, R., Zhang, Q., Xu, J.: Convergence of Discrete-time Cellular Neural Networks. Chinese J. Electronics 11, 352–356 (2002)
Ma, R., Liu, N., Xu, J.: Stability Conditions for Discrete Hopfield Neural Networks with Delay. Acta Electronica Sinica 32, 1674–1677 (2004)
Qiu, S., Tang, E.-C.C., Yeung, D.S.: Stability of Discrete Hopfield Neural Networks with Time-delay. In: Proceedings of IEEE International Conference on System, Man Cybernetics, pp. 2546–2552 (2000)
Ma, R., Xi, Y., Lei, S.: Dynamic Behavior of Discrete Hopfield Neural Networks with Time-Delay. Chinese J. Electronics 14, 187–191 (2005)
Ma, R., Lei, S., Zhang, S.: Dynamic Behavior Analysis of Discrete Neural Networks with Delay. In: Wang, J., Liao, X.-F., Yi, Z. (eds.) ISNN 2005. LNCS, vol. 3496, pp. 259–264. Springer, Heidelberg (2005)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2006 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Ma, RN., Bai, GQ. (2006). Stability Conditions for Discrete Hopfield Neural Networks with Delay. In: Huang, DS., Li, K., Irwin, G.W. (eds) Intelligent Computing. ICIC 2006. Lecture Notes in Computer Science, vol 4113. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11816157_59
Download citation
DOI: https://doi.org/10.1007/11816157_59
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-37271-4
Online ISBN: 978-3-540-37273-8
eBook Packages: Computer ScienceComputer Science (R0)