Abstract
This paper investigates global exponential stability of a class of Hopfield neural networks with delays based on contraction mapping principle, Lyapunov function and inequality technique. Some sufficient conditions are derived that ensure the existence, uniqueness, global exponential stability of equilibrium point of the neural networks. Finally, an illustrative numerical example is given to demonstrate the effectiveness of our results.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Zhong S, Liu B, Wang X, Fan X (2008) Stability theory of neural networks. Science Press, Beijing in Chinese
Gopalsamy K, He X (1994) Stability in asymmetric Hopfield nets with transmission delays. Physica D 76:344–358
Zhou Q (2009) Global exponential stability of BAM neural networks with distributed delays and impulses. Nonlinear Anal Real World Appl 10:144–153
Tan Y, Tan M (2009) Global asymptotical stability of continuous-time delayed neural networks without global Lipschitz activation functions. Commun Nonlinear Sci Numer Simulat 14:3715–3722
Zhou J, Li S (2009) Global exponential stability of impulsive BAM neural networks with distributed delays. Neurocomputing 72:1688–1693
Ahmada S, Stamov I (2008) Global exponential stability for impulsive cellular neural networks with time-varying delays. Nonlinear Anal Real World Appl 69:786–795
Xia Y, Huang Z, Han M (2008) Exponential p-stability of delayed Cohen-Grossberg type BAM neural networks with impulses. Chaos Solitons Fractals 38:806–818
Long S, Xu D (2008) Delay-dependent stability analysis for impulsive neural networks with time-varying delays. Neurocomputing 71:1705–1713
Cheng L, Hou Z, Tan M (2009) A delayed projection neural network for solving linear variational inequalities. IEEE Trans Neural Netw 20:915–925
Cheng L, Hou Z, Tan M (2008) A neutral-type delayed projection neural network for solving nonlinear variational inequalities. IEEE Trans Circuits Syst II: Express Briefs 55:806–810
Zeng Z, Wang J (2008) Design and analysis of high-capacity associative memories based on a class of discrete-time recurrent neural networks. IEEE Trans Syst Man Cybern B Cybern 38(6):1525–1536
Zeng Z, Huang D, Wang Z (2005) Global stability of a general class of discrete-time recurrent neural networks. Neural Process Lett 22(1):33–47
Zeng Z, Huang D, Wang Z (2005) Memory pattern analysis of cellular neural network. Phys Lett A 342(1–2):114–128
Acknowledgments
The authors would like to thank the anonymous reviewers and the editor for their constructive comments that led to truly significant improvement of the manuscript. The work is supported by Key Science Foundations of Educational Department of Hubei Province under Grant D20082201 and Z20062202, Youth Project of Educational Department of Hubei Province under Grant Q20102508, Key Project of Chinese Ministry of Education (NO:209078), Innovation Teams of Hubei Normal University.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Liu, W., Fu, C. & Hu, H. Global exponential stability of a class of Hopfield neural networks with delays. Neural Comput & Applic 20, 1205–1209 (2011). https://doi.org/10.1007/s00521-010-0470-9
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00521-010-0470-9