×
Zeng, Zhigang; Huang, De-Shuang; Wang, Zengfu

Memory pattern analysis of cellular neural networks. (English) Zbl 1222.92013

Phys. Lett., A 342, No. 1-2, 114-128 (2005).
Summary: We have shown that \(n\)-dimensional cellular neural networks and delay cellular neural networks can have no more than \(3n\) memory patterns, and \(2n\) memory patterns which are locally exponentially stable.We have obtained estimates of the attractive domain of such \(2n\) locally exponentially stable memory patterns. In addition, we have derived conditions that the equilibrium point is locally exponentially stable when the equilibrium point is at the designated position. Some sufficient conditions have been obtained to guarantee the global exponential stability for the cellular neural networks. These conditions can be directly derived from the parameters of the neural networks, and are very easy to be verified. The results are improvements and extensions of existing ones. Finally, the validity and performance of the results are illustrated by two simulation results.

Cited in 22 Documents

MSC:

92B20 Neural networks for/in biological studies, artificial life and related topics

Keywords:

stability; equilibrium; attractive domain
PDF BibTeX XML Cite
\textit{Z. Zeng} et al., Phys. Lett., A 342, No. 1--2, 114--128 (2005; Zbl 1222.92013)
Full Text: DOI
  • logo of hbz
  • logo of WorldCat

References:

[1] Hopfield, J.J., Proc. natl. acad. sci., 81, 3088, (1984)
[2] Chua, L.O.; Roska, T., IEEE trans. circuits systems, 37, 1520, (1990)
[3] Chua, L.O.; Roska, T., Int. J. circuit theory appl., 20, 449, (1992)
[4] Roska, T.; Wu, C.W.; Balsi, M.; Chua, L.O., IEEE trans. circuits systems I, 39, 487, (1992)
[5] Roska, T.; Wu, C.W.; Chua, L.O., IEEE trans. circuits systems I, 40, 270, (1993)
[6] Civalleri, P.P.; Gilli, M.; Pandolfi, L., IEEE trans. circuits systems I, 40, 157, (1993)
[7] Liao, X.; Wang, J., IEEE trans. circuits systems I, 50, 268, (2003)
[8] Takahashi, N., IEEE trans. circuits systems I, 47, 793, (2000)
[9] Zeng, Z.; Wang, J.; Liao, X., IEEE trans. circuits systems I, 50, 1353, (2003)
[10] Yi, Z.; Heng, A.; Leung, K.S., IEEE trans. circuits systems I, 48, 680, (2001)
[11] Liao, T.L.; Wang, F.C., IEEE trans. neural networks, 11, 1481, (2000)
[12] Cao, J., IEEE trans. circuits systems I, 48, 1330, (2001)
[13] Dong, M., Phys. lett. A, 300, 49, (2002)
[14] Cao, J., Phys. lett. A, 307, 136, (2003)
[15] Li, X.M.; Huang, L.H.; Zhu, H., Nonlinear anal., 53, 319, (2003)
[16] Jiang, H.; Li, Z.; Teng, Z., Phys. lett. A, 306, 313, (2003)
[17] Yu, G.-J.; Lu, C.-Y.; Tsai, J.S.-H.; Su, T.-J.; Liu, B.-D., IEEE trans. circuits systems I, 50, 677, (2003)
[18] Liao, X., Sci. China A, 24, 902, (1994)
[19] Arik, S.; Tavsanoglu, V., IEEE trans. circuits systems I, 45, 168, (2000)
[20] Arik, S., IEEE trans. circuits systems I, 47, 571, (2000)
[21] Mohamad, S.; Gopalsamy, K., Appl. math. comput., 135, 17, (2003)
[22] Arik, S., IEEE trans. circuits systems I, 49, 1211, (2002)
[23] Arik, S., IEEE trans. neural networks, 13, 1239, (2002)
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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.