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)
Global exponential stability of impulsive cellular neural networks with time-varying and distributed delay. (English) Zbl 1198.34154
Summary: A model of impulsive cellular neural networks with time-varying and distributed delays is investigated. By establishing an integro-differential inequality with impulsive initial conditions and employing the $M$-matrix theory, some sufficient conditions ensuring the existence, uniqueness and global exponential stability of equilibrium point for impulsive cellular neural networks with time-varying and distributed delays are obtained. An example is given to show the effectiveness of the results obtained here. Editorial remark: There are doubts about a proper peer-reviewing procedure of this journal. The editor-in-chief has retired, but, according to a statement of the publisher, articles accepted under his guidance are published without additional control.

MSC:
34K20Stability theory of functional-differential equations
92B20General theory of neural networks (mathematical biology)
WorldCat.org
Full Text: DOI
References:
[1] Chua, L. O.; Yang, L.: Cellular neural networks: theory, IEEE trans circuits syst I. 35, No. 10, 1257-1272 (1988) · Zbl 0663.94022 · doi:10.1109/31.7600
[2] Roska, T.; Chua, L. O.: Cellular neural networks with nonlinear and delay-type template elements nonuniform grids, Int J circuit theory appl 20, 469-481 (1992) · Zbl 0775.92011 · doi:10.1002/cta.4490200504
[3] Cao, J.: Global stability analysis in delayed cellular neural networks, Phys rev E 59, No. 5, 5940-5944 (1999)
[4] Cao, J.: A set of stability criteria for delayed cellular neural networks, IEEE trans circuits syst I 48, 494-498 (2001) · Zbl 0994.82066 · doi:10.1109/81.917987
[5] Arik, S.; Tavsanoglu, V.: Equilibrium analysis of delayed cnns, IEEE trans circuits syst I 45, No. 2, 168-171 (1998) · Zbl 0917.68223
[6] Singh, V.: A generalized LMI-based approach to the global asymptotic stability of delayed cellular neural networks, IEEE trans neural networks 15, No. 1, 223-225 (2004)
[7] Zhang, Q.; Wei, X.; Xu, J.: Stability analysis for cellular neural networks with variable delays, Chaos, solitons & fractals 28, No. 2, 331-336 (2006) · Zbl 1084.34068
[8] Zhang, Q.; Wei, X.; Xu, J.: Global exponential stability of Hopfield neural networks with continuously distributed delays, Phys lett A 315, 431-436 (2003) · Zbl 1038.92002 · doi:10.1016/S0375-9601(03)01106-X
[9] Park, Ju H.; Cho, H. J.: A delay-dependent asymptotic stability criterion of cellular neural networks with timevarying discrete and distributed delays, Chaos, solitons & fractals 33, 436-442 (2007) · Zbl 1142.34379 · doi:10.1016/j.chaos.2006.01.015
[10] Zhao, H.: Global asymptotic stability of Hopfield neural network involving distributed delays, Neural networks 17, 47-53 (2004) · Zbl 1082.68100 · doi:10.1016/S0893-6080(03)00077-7
[11] Liao, X.; Wong, K. -W.; Li, C.: Global exponential stability for a class of generalized neural networks with distributed delays, Nonlinear anal: real world appl 5, 527-547 (2004) · Zbl 1094.34053 · doi:10.1016/j.nonrwa.2003.12.002
[12] Liang, J.; Cao, J.: Global asymptotic stability of bi-directional associative memory networks with distributed delays, Appl math comput 152, 415-424 (2004) · Zbl 1046.94020 · doi:10.1016/S0096-3003(03)00567-8
[13] Zhang, J.; Suda, Y.; Iwasa, T.: Absolutely exponential stability of a class of neural networks with unbounded delay, Neural networks 17, 391-397 (2004) · Zbl 1074.68057 · doi:10.1016/j.neunet.2003.09.005
[14] Liao, X.; Li, C.; Wong, K. -W.: Criteria for exponential stability of Cohen -- Grossberg neural networks, Neural networks 17, 1401-1414 (2004) · Zbl 1073.68073 · doi:10.1016/j.neunet.2004.08.007
[15] Wang, L.: Stability of Cohen -- Grossberg neural networks with distributed delays, Appl math comput 160, 93-110 (2005) · Zbl 1069.34113 · doi:10.1016/j.amc.2003.09.014
[16] Wan, L.; Sun, J.: Global asymptotic stability of Cohen -- Grossberg neural network with continuously distributed delays, Phys lett A 342, 331-340 (2005) · Zbl 1222.93200 · doi:10.1016/j.physleta.2005.05.026
[17] Gopalsamy, K.; He, X.: Delay-independent stability in bidirectional associative memory networks, IEEE trans neural networks 5, 998-1002 (1994)
[18] Gopalsamy, K.: Stability of artificial neural networks with impulses, Appl math comput 154, 783-813 (2004) · Zbl 1058.34008 · doi:10.1016/S0096-3003(03)00750-1
[19] Guan, Z.; Chen, G.: On delayed impulsive Hopfield neural networks, Neural networks 12, 273-280 (1999)
[20] Guan, Z.; James, L.; Chen, G.: On impulsive auto-associative neural networks, Neural networks 13, 63-69 (2000)
[21] Akca, H.; Alassar, R.; Covachev, V.; Covacheva, Z.; Al-Zahrani, E.: Continuous-time additive Hopfield-type neural networks with impulses, J math anal appl 290, 436-451 (2004) · Zbl 1057.68083 · doi:10.1016/j.jmaa.2003.10.005
[22] Li, Y.; Lu, L.: Global exponential stability and existence of periodic solution of Hopfield-type neural networks with impulses, Phys lett A 333, 62-71 (2004) · Zbl 1123.34303 · doi:10.1016/j.physleta.2004.09.083
[23] Li, Y.: Global exponential stability of BAM neural networks with delays and impulses, Chaos, solitions & fractals 24, 279-285 (2005) · Zbl 1099.68085
[24] Li, Y.; Xing, W.; Lu, L.: Existence and global exponential stability of periodic solution of a class of neural networks with impulses, Chaos, solitons & fractals 27, 437-445 (2006) · Zbl 1084.68103
[25] Li, Y.; Yang, C.: Global exponential stability analysis on impulsive BAM neural networks with distributed delays, J math anal appl 324, 1125-1139 (2006) · Zbl 1102.68117 · doi:10.1016/j.jmaa.2006.01.016
[26] Yang, Y.; Cao, J.: Stability and periodicity in delayed cellular neural networks with impulsive effects, Nonlinear anal: real world appl 8, 362-374 (2007) · Zbl 1115.34072 · doi:10.1016/j.nonrwa.2005.11.004
[27] Xu, D.; Yang, Z.: Impulsive delay differential inequality and stability of neural networks, J math anal appl 305, 107-120 (2005) · Zbl 1091.34046 · doi:10.1016/j.jmaa.2004.10.040
[28] Xu, D.; Zhu, W.; Long, S.: Global exponential stability of impulsive integro-differential equation, Nonlinear anal 64, 2805-2816 (2006) · Zbl 1093.45004 · doi:10.1016/j.na.2005.09.020
[29] Yang, Z.; Xu, D.: Impulsive effects on stability of Cohen -- Grossberg neural networks with variable delays, Appl math comput 177, 63-78 (2006) · Zbl 1103.34067 · doi:10.1016/j.amc.2005.10.032
[30] Chen, Z.; Ruan, J.: Global stability analysis of impulsive Cohen -- Grossberg neural networks with delay, Phys lett A 345, 101-111 (2005) · Zbl 05314183
[31] Chen, Z.; Ruan, J.: Global dynamic analysis of general Cohen -- Grossberg neural networks with impulse, Chaos, solitons & fractals 32, 1830-1837 (2007) · Zbl 1142.34045 · doi:10.1016/j.chaos.2005.12.018
[32] Liao, X.; Li, C.: Global attractivity of Cohen -- Grossberg model with finite and infinite delays, J math anal appl 315, 244-262 (2006) · Zbl 1098.34062 · doi:10.1016/j.jmaa.2005.04.076
[33] Song, Q.; Cao, J.: Stability analysis of Cohen -- Grossberg neural network with both time-varying and continuously distributed delays, J comp appl math 197, 188-203 (2006) · Zbl 1108.34060 · doi:10.1016/j.cam.2005.10.029
[34] Berman, A.; Plemmons, R. J.: Nonnegative matrices in mathematical sciences, (1979) · Zbl 0484.15016
[35] Lakshmikantham, V.; Bainov, D. D.; Simeonov, P. S.: Theory of impulsive differential equations, (1989) · Zbl 0718.34011
[36] Zhang, J.; Suda, Y.; Iwasa, T.: Absolutely exponential stability of a class of neural networks with unbounded delay, Neural networks 17, 391-397 (2004) · Zbl 1074.68057 · doi:10.1016/j.neunet.2003.09.005