Abstract
The stability of neural networks is fundamental for successful applications of the networks. In this paper, the exponential stability of Cohen-Grossberg Neural Networks is investigated. To avoid the difficulty of the construction of a proper Lyapunov function, a new concept named generalized relative nonlinear measure is introduced, and thus a novel approach to stability analysis of neural networks is developed. With this new approach, sufficient conditions for the existence, uniqueness of the equilibrium and the exponential stability of the Cohen-Grossberg neural networks are presented. Meanwhile, the exponential convergence rate of the networks to stable equilibrium point is estimated, and the attraction region of local stable equilibrium point is also characterized.
This is a preview of subscription content, log in via an institution to check access.
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
Fang, Y., Kincaid, T.G.: Stability Analysis of Dynamical Neural Networks. IEEE Transactions on Neural Networks 7(4), 996–1006 (1996)
Forti, M., Manetti, S., Marini, M.: Necessary and Sufficient Condition for Absolute Stability of Neural Networks. IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications 41(7), 491–494 (1994)
Truccolo, W.A., Rangarajan, G., Chen, Y.H., Ding, M.Z.: Analyzing Stability of Equilibrium Points in Neural Networks: A General Approach. Neural Networks 16(10), 1453–1460 (2003)
Qiao, H., Peng, J.G., Xu, Z.B., Zhang, B.: A Reference Model Approach to Stability Analysis of Neural Networks. IEEE Transactions on Systems, Man and Cybernetics, Part B 33(6), 925–936 (2003)
Cohen, M.A., Grossberg, S.: Absolute Stability of Global Pattern Formation and Parallel Memory Storage by Competitive Neural Networks. IEEE Transactions on Systems, Man and Cybernetics SMC-13(5), 815–821 (1983)
Wang, L., Zou, X.F.: Exponential Stability of Cohen-Grossberg Neural Networks. Neural Networks 15, 415–422 (2002)
Chen, T.P., Rong, L.B.: Robust Global Exponential Stability of Cohen-Grossberg Neural Networks with Time Delays. IEEE Transactions on Neural Networks 15(1), 203–206 (2004)
Ye, H., Michel, A.N., Wang, K.: Qualitative Analysis of Cohen-Grossberg Neural Network with Multiple Delays. Physical Review E 51, 2611–2618 (1995)
Hwang, C.C., Cheng, C.J., Liao, T.L.: Globally Exponential Stability of Generalized Cohen-Grossberg Neural Networks with Delays. Physics Letters A 319(1-2), 157–166 (2003)
Tank, D.W., Hopfield, J.J.: Simple “Neural” Optimization Networks: An A/D Converter, Signal Decision Circuit, and a Linear Programming Circuit. IEEE Transactions on Circuits and Systems 33(5), 533–541 (1986)
Qiao, H., Peng, J.G., Xu, Z.B.: Nonlinear Measures: A New Approach to Exponential Stability Analysis for Hopfield-Type Neural Networks. IEEE Transactions of Neural Networks 12(2), 360–370 (2001)
Peng, J.G., Xu, Z.B.: On Asymptotic Behaviours of Nonlinear Semigroup of Lipschitz Operators with Applications. Acta Mathematica Sinica 45(6), 1099–1106 (2002)
Söderlind, G.: Bounds on Nonlinear Operators in Finite-Dimensional Banach Spaces. Numerische Mathematik 50, 27–44 (1986)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2004 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Wan, A., Mao, W., Zhao, C. (2004). A Novel Approach to Exponential Stability Analysis of Cohen-Grossberg Neural Networks. In: Yin, FL., Wang, J., Guo, C. (eds) Advances in Neural Networks – ISNN 2004. ISNN 2004. Lecture Notes in Computer Science, vol 3173. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-28647-9_16
Download citation
DOI: https://doi.org/10.1007/978-3-540-28647-9_16
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-22841-7
Online ISBN: 978-3-540-28647-9
eBook Packages: Springer Book Archive