Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 33122
An Analysis of Global Stability of Cohen-Grossberg Neural Networks with Multiple Time Delays
Authors: Zeynep Orman, Sabri Arik
Abstract:
This paper presents a new sufficient condition for the existence, uniqueness and global asymptotic stability of the equilibrium point for Cohen-Grossberg neural networks with multiple time delays. The results establish a relationship between the network parameters of the neural system independently of the delay parameters. The results are also compared with the previously reported results in the literature.Keywords: Equilibrium and stability analysis, Cohen-Grossberg Neural Networks, Lyapunov Functionals.
Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1330159
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1388References:
[1] M.A. Cohen and S. Grossberg, "Absolute stability and global pattern formation and parallel memory storage by competitive neural networks", IEEE Trans. Systems, Man and Cybernetics, vol. 13, pp. 815-821, 1983.
[2] H.Ye, A. N. Michel, and K. Wang, "Qualitative analysis of Cohen-Grossberg neural networks with multiple delays", Physical Review E, vol. 51, pp. 2611-2618, March 1995.
[3] X.Liao, C. Li, and K. Wong, "Criteria for exponential stability of Cohen-Grossberg neural networks", Neural Networks, vol. 17, pp. 1401-1414, August 2004.
[4] J.Liu, "Global exponential stability of Cohen-Grossberg neural networks with time-varying delays", Chaos Solitons and Fractals, vol. 26, pp. 935-945, January 2005.
[5] M. Forti and A. Tesi, "New conditions for global stability of neural networks with applications to linear and quadratic programming problems", IEEE Trans. Circuits Syst., vol. 42, no. 7, pp. 354-365, July 1995.
[6] Q.K. Song , J.D. Cao , "Stability analysis of Cohen-Grossberg neural network with both time-varying and continuously distributed delays", Journal of Computational and Applied Mathematics, vol. 197, no. 1, pp. 188-203, December 2006.
[7] S. Arik, V. Tavsanoglu, "On the global asymptotic stability of delayed cellular neural networks", IEEE Trans. Circuits and Syst.I, vol. 47, no. 5, pp. 571-574, April 2000.
[8] X.Y. Lou, B.T. Cui, "Global exponential stability analysis of delayed Cohen-Grossberg neural networks with distributed delays", International Journal of Systems Science, vol. 38 pp. 601-609, 2007.
[9] W. Yu, J. Cao and J. Wang, "An LMI approach to global asymptotic stability of the delayed Cohen-Grossberg neural network via nonsmooth analysis", Neural Networks, vol. 20, pp. 810-818, Sep 2007.
[10] T.W. Huang, C.D. Li, G. Chen, "Stability of Cohen-Grossberg neural networks with unbounded distributed delays", Chaos Solitons and Fractals, vol. 34, pp. 992-996, Nov 2007.
[11] H. Huang, J. Cao and J. Wang, "Global exponential stability and periodic solutions of recurrent neural networks with delays", Physics Letters A, vol. 298, pp. 393-404, June 2002.
[12] Z.H. Yuan, L.F. Yuan and L.H. Huang , "Dynamics of periodic Cohen- Grossberg neural networks with varying delays", Neurocomputing, vol. 70, pp. 164-172, Dec 2006.
[13] C. C. Hwang, C. J. Cheng and T. L. Liao, "Globally exponential stability of generalized Cohen-Grossberg neural networks with delays ," Physics Letters A, vol. 319, pp. 157-166, 2003.
[14] H. K. Khalil, Nonlinear Systems, Mcmillan Publishing Company, New York, 1988