zbMATH — the first resource for mathematics

Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
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.

34K60Qualitative investigation and simulation of models
34K20Stability theory of functional-differential equations
68T05Learning and adaptive systems
Full Text: DOI
[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, No. 2, 229 (1989)
[6] Forti, M.; Tesi, A.: IEEE trans. Circuits systems I. 42, No. 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, No. 4, 571 (2000)
[10] Arik, S.: IEEE trans. Circuits systems I. 47, No. 7, 1089 (2000)
[11] Den Driessche, P. Van; Zou, X.: SIAM J. Appl. math.. 58, No. 6, 1878 (1998)
[12] Zhang, J.; Jin, X.: Neural networks. 13, No. 7, 745 (2000)
[13] Zhang, J.: Comput. math. Appl.. 45, 1707 (2003)
[14] Zhang, J.: IEEE trans. Circuits systems I. 50, No. 2, 288 (2003)
[15] Zhang, J.: Int. J. Circuit theory appl.. 30, 395 (2002)
[16] Chen, T.: Neural networks. 14, 977 (2001) · Zbl 0992.34059
[17] Ye, H.; Michel, A.; Wang, K.: Phys. rev. E. 51, 2611 (1995)
[18] Wang, L.; Zou, X.: Neural networks. 15, 415 (2002) · Zbl 1025.92002
[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) · Zbl 0384.93002