Abstract
This paper studies the global convergence properties of Cohen-Grossberg neural networks with discrete time delays. Without assuming the symmetry of interconnection weight coefficients, and the monotonicity and differentiability of activation functions, and by employing Lyapunov functionals, we derive new delay independent sufficient conditions under which a delayed Cohen-Grossberg neural network converges to a globally asymptotically stable equilibrium point. Some examples are given to illustrate the advantages of the results over the previously reported results in the literature.
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Cohen, M.A., Grossberg, S.: Absolute stability and global pattern formation and parallel memory storage by competitive neural networks. IEEE Trans. Systems, Man and Cybernetics 13, 815–821 (1983)
Ye, H., Michel, A.N., Wang, K.: Qualitative analysis of Cohen-Grossberg neural networks with multiple delays. Physical Review E 51, 2611–2618 (1995)
Forti, M., Tesi, A.: New conditions for global stability of neural networks with applications to linear and quadratic programming problems. IEEE Trans. Circuits Syst. I 42(7), 354–365 (1995)
Arik, S., Tavsanoglu, V.: Equilibrium analysis of delayed CNNs. IEEE Trans. Circuits and Syst. I 45, 168–171 (1998)
Arik, S., Tavsanoglu, V.: On the global asymptotic stability of delayed cellular neural networks. IEEE Trans. Circuits and Syst. I 47(5), 571–574 (2000)
Liao, T.-L., Wang, F.-C.: Global stability for cellular neural networks with time delay. IEEE Trans. on Neural Networks 11, 1481–1485 (2000)
Takahashi, N.: A new sufficient condition for complete stability of cellular neural networks with delay. IEEE Trans. Circuits and Syst. I 47, 793–799 (2000)
Yi, Z., Heng, P.A., Leung, K.S.: Convergence Analysis of Delayed Cellular Neural Networks with Unbounded Delay. IEEE Trans. on Circuits and Syst. I 48, 680–687 (2001)
Huang, H., Cao, J., Wang, J.: Global exponential stability and periodic solutions of recurrent neural networks with delays. Physics Letters A 298, 393–404 (2002)
Sun, C., Zhang, K., Fei, S., Feng, C.B.: On exponential stability of delayed neural networks with a general class of activation functions. Physics Letters A 298, 122–132 (2002)
Hwang, C.C., Cheng, C.J., Liao, T.L.: Globally exponential stability of generalized Cohen-Grossberg neural networks with delays. Physics Letters A 319, 157–166 (2003)
Xiaong, W., Cao, J.: Absolutely exponential stability of CohenGrossberg neural networks with unbounded delays. Neurocomputing 68, 1–12 (2005)
Arik, S., Tavsanoglu, V.: Global asymptotic stability analysis of bidirectional associative memory neural networks with constant time delays. Neurocomputing 68, 161–176 (2005)
Arik, S., Orman, Z.: Global stability analysis of CohenGrossberg neural networks with time varying delays. Physics Letters A 341, 410–421 (2005)
Liao, X., Li, C.: An LMI approach to asymptotical stability of multi-delayed neural networks. Physica D: Nonlinear Phenomena 200, 139–155 (2005)
Sun, J., Wan, L.: Global exponential stability and periodic solutions of CohenGrossberg neural networks with continuously distributed delays. Physica D: Nonlinear Phenomena 208, 1–20 (2005)
He, Y., Wang, Q.G., Wu, M.: LMI-based stability criteria for neural networks with multiple time-varying delays. Physica D: Nonlinear Phenomena 212, 126–136 (2005)
Cao, J., Li, X.: Stability in delayed CohenGrossberg neural networks: LMI optimization approach. Physica D: Nonlinear Phenomena 212, 54–65 (2005)
Liao, X., Li, C., Wong, K.: Criteria for exponential stability of Cohen-Grossberg neural networks. Neural Networks 17, 1401–1414 (2004)
Liu, J.: Global exponential stability of Cohen-Grossberg neural networks with timevarying delays. Chaos Solitons and Fractals 26, 935–945 (2005)
Khalil, H.K.: Nonlinear Systems. Mcmillan Publishing Company, New York (1988)
Horn, R.A., Johnson, C.R.: Topics in Matrix Analyis. Cambridge University Press, Cambridge (1991)
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
Orman, Z., Arik, S. (2006). New Results for Global Stability of Cohen-Grossberg Neural Networks with Discrete Time Delays. In: King, I., Wang, J., Chan, LW., Wang, D. (eds) Neural Information Processing. ICONIP 2006. Lecture Notes in Computer Science, vol 4232. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11893028_64
Download citation
DOI: https://doi.org/10.1007/11893028_64
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-46479-2
Online ISBN: 978-3-540-46480-8
eBook Packages: Computer ScienceComputer Science (R0)