zbMATH — the first resource for mathematics

Examples
 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.

Operators
 a & b logic and a | b logic or !ab logic not abc* right wildcard "ab c" phrase (ab c) parentheses
Fields
 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)
Existence and exponential stability of almost periodic solutions for cellular neural networks with mixed delays. (English) Zbl 1139.34319
Summary: Cellular neural networks with mixed delays are considered. Sufficient conditions for the existence and exponential stability of the almost periodic solutions are established by using fixed point theorem, Lyapunov functional method and differential inequality technique.

MSC:
 34K14 Almost and pseudo-periodic solutions of functional differential equations 34K20 Stability theory of functional-differential equations 92B20 General theory of neural networks (mathematical biology)
Full Text:
References:
 [1] Cao, J.: Global exponential stability and periodic solutions of delayed cellular neural networks. J comput syst sci 60, 38-46 (2000) · Zbl 0988.37015 [2] Cao, J.: New results concerning exponential stability and periodic solutions of delayed cellular neural networks with delays. Phys lett A 307, 136-147 (2003) · Zbl 1006.68107 [3] Huang, H.; Cao, J.; Wang, J.: Global exponential stability and periodic solutions of recurrent cellular neural networks with delays. Phys lett A 298, 393-404 (2002) · Zbl 0995.92007 [4] Dong, Q.; Matsui, K.; Huang, X.: Phys lett A. 298, 393-404 (2002) [5] Guo, S.; Huang, L.: Periodic solutions in an inhibitory two-neuron network. J comput appl math 161, 217-229 (2003) · Zbl 1044.34034 [6] Liu, Z.; Chen, A.: Existence and global exponential stability of periodic solutions of cellular neural networks with time-vary delays. J math anal appl 290, 247-262 (2004) · Zbl 1055.34135 [7] Guo, S.; Huang, L.: Stability analysis of a delayed Hopfield neutral network. Phys rev E 67, 061902 (2003) [8] Chen, A.; Huang, L. H.: Existence and attractivity of almost periodic solutions of Hopfield neutral networks. Math acta scientia 21A, No. 4, 505-511 (2001) · Zbl 0989.92001 [9] Liu, Z.; Chen, A.; Cao, J.; Huang, L.: Existence and global exponential stability of almost periodic solutions of BAM neural networks with continuously distributed delays. Phys lett A 319, 305-316 (2003) · Zbl 1045.82017 [10] Huang, X.; Cao, J.: Almost periodic solutions of inhibitory cellular neural networks with time-vary delays. Phys lett A 314, 222-231 (2003) · Zbl 1052.82022 [11] Chen, A.; Cao, J.: Existence and attractivity of almost periodic solutions for cellular neural networks with distributed delays and variable coefficients. Appl math comput 134, 125-140 (2003) · Zbl 1035.34080 [12] Liu, B.; Huang, L.: Existence and exponential stability of almost periodic solutions for cellular neural networks with time-varying delays. Phys lett A 341, 135-144 (2005) · Zbl 1171.82329 [13] Berman, A.; Plemmons, R. J.: Nonnegative matrices in the mathematical science. (1979) · Zbl 0484.15016 [14] Fink, A. M.: Almost periodic differential equations. Lecture notes in mathematics 377 (1974) · Zbl 0325.34039 [15] He, C. Y.: Almost periodic differential equation. (1992) [16] Hale, J.; Lunel, S. M. Verduyn: Introduction to functional differential equations. (1993) · Zbl 0787.34002 [17] Lasalle, J. P.: The stability of dynamical system. (1976) · Zbl 0364.93002