×

Global exponential stability of Cohen-Grossberg neural networks with variable delays. (English) Zbl 1136.34347

Summary: In this Letter, the conditions ensuring existence, uniqueness of the equilibrium point of Cohen-Grossberg neural networks with variable delays are obtained under more general assumption about activation functions. Applying idea of vector Lyapunov function, and M-matrix theory, the sufficient conditions for global exponential stability of Cohen-Grossberg neural networks are obtained. These results generalize a few previous known results and remove some restrictions on the neural networks.

MSC:

34K60 Qualitative investigation and simulation of models involving functional-differential equations
34K20 Stability theory of functional-differential equations
68T05 Learning and adaptive systems in artificial intelligence
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Cohen, M. A.; Grossberg, S., IEEE Trans. Systems Man Cybernet., 13, 815 (1983)
[2] Hopfield, J. J.; Tank, D. W., Proc. Natl. Acad. Sci. USA, 81, 3088 (1984)
[3] Kennedy, M. P.; Chua, L. O., IEEE Trans. Circuits Systems, 35, 554 (1988)
[4] Morita, M., Neural Networks, 6, 115 (1993)
[5] Michel, A. N.; Farrell, J. A.; Porod, W., IEEE Trans. Circuits Systems, 36, 2, 229 (1989)
[6] Forti, M.; Tesi, A., IEEE Trans. Circuits Systems I, 42, 7, 354 (1995)
[7] Marcus, C. M.; Westervelt, R. M., Phys. Rev. A, 39, 347 (1989)
[8] Gopalsamy, K.; He, X., Physica D, 76, 344 (1994)
[9] Arik, S.; Tavsanoglu, V., IEEE Trans. Circuits Systems I, 47, 4, 571 (2000)
[10] Arik, S., IEEE Trans. Circuits Systems I, 47, 7, 1089 (2000)
[11] Van Den Driessche, P.; Zou, X., SIAM J. Appl. Math., 58, 6, 1878 (1998)
[12] Zhang, J.; Jin, X., Neural Networks, 13, 7, 745 (2000)
[13] Zhang, J., Comput. Math. Appl., 45, 1707 (2003)
[14] Zhang, J., IEEE Trans. Circuits Systems I, 50, 2, 288 (2003)
[15] Zhang, J., Int. J. Circuit Theory Appl., 30, 395 (2002)
[16] Chen, T., Neural Networks, 14, 977 (2001)
[17] Ye, H.; Michel, A.; Wang, K., Phys. Rev. E, 51, 2611 (1995)
[18] Wang, L.; Zou, X., Neural Networks, 15, 415 (2002)
[19] Chen, T.; Rong, L., Phys. Lett. A, 317, 436 (2003)
[20] Hwang, C. C.; Cheng, C. J.; Liao, T. L., Phys. Lett. A, 319, 157 (2003)
[21] Chen, T.; Rong, L., IEEE Trans. Neural Networks, 15, 203 (2004)
[22] Siljak, D. D., Large-Scale Dynamic Systems—Stability and Structure (1978), Elsevier: Elsevier New York · Zbl 0382.93003
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.