Abstract
In the paper, the reaction-diffusion neural network models with both variable time delays and unbounded delay are investigated. These models contain weaker activation functions than partially or globally Lipschitz continuous functions. Without assuming the boundedness, monotonicity and differentiability of the active functions, algebraic criteria ensuring existence, uniqueness and global exponential stability of the equilibrium point are obtained.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Chua, L.O., Yang, L.: Cellular Neural Networks: Theory. IEEE Transactions on Circuits and Systems 35, 1257–1272 (1988)
Forti, M., Tesi, A.: New Conditions for Global Stability of Neural Networks with Application to Linear and Quadratic Programming Problems. IEEE Trans. Circuits System-I. 42, 354–366 (1995)
Zheng, W., Zhang, J.: Global Exponential Stability of a Class of Neural Networks with Variable Delays. Computers and Mathematics with Applications 49, 895–902 (2005)
Zhang, J.: Globally Exponential Stability of Neural Networks with Variable Delays. IEEE Transactions on Circuits and Systems-I 2, 288–291 (2003)
Zhang, J., Suda, Y., Iwasa, T.: Absolutely Exponential Stability of a Class of Neural Networks with Unbounded Delay. Neural Networks 17, 391–397 (2004)
Liao, X., Fu, Y.: Stability of Hopfield Neural Networks with Reaction-Diffusion Terms. Acta Electronica Sinica 1, 78–80 (2000)
Wang, L., Xu, D.: Global Stability of Reaction-Diffusion Hopfield Neural Networks with Variable Time Delay. Science in China (serial E) 6, 488–495 (2003)
Liang, J., Cao, J.: Global Exponential Stability of Reaction-Diffusion Recurrent Neural Networks with Time-Varying Delays. Physics letters A 314, 434–442 (2003)
Song, Q., Cao, J.: Global Exponential Stability and Existence of Periodic Solutions in BAM Networks with Delays and Reaction-Diffusion Terms. Chaos Solitons and Fractals 23, 421–430 (2005)
Song, Q., Zhao, Z., Li, Y.: Global Exponential Stability of BAM Neural Networks with Distributed Delays and Reaction-Diffusion Terms. Physics Letters A 335, 213–225 (2005)
Siljak, D.D.: Large-Scale Dynamic Systems — Stability and Structure. Elsevier North-Holland, Inc., New York (1978)
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
Zheng, W., Zhang, J., Zhang, W. (2006). Global Exponential Stability of Reaction-Diffusion Neural Networks with Both Variable Time Delays and Unbounded 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_43
Download citation
DOI: https://doi.org/10.1007/11816157_43
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)