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Erschienen in: Neural Processing Letters 1/2018

02.06.2017

Stability Analysis of Impulsive Neural Networks with Piecewise Constant Arguments

verfasst von: Tianhu Yu, Dengqing Cao

Erschienen in: Neural Processing Letters | Ausgabe 1/2018

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Abstract

The global exponential stability problem is considered for a class of impulsive neural networks with piecewise constant arguments in this paper. By employing the Banach fixed point theorem and the Razumikhin-type technique, stability criterion is obtained for the existence, uniqueness and global exponential stability of the periodic solution. Typical numerical examples are given to illustrate the improvement in less conservatism of the results.

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Literatur
1.
Zurück zum Zitat Chua LO, Roska T (1992) Cellular neural networks with nonlinear and delay type template elements and non-uniform grids. Int J Circuit Theory Appl 20:449–451CrossRefMATH Chua LO, Roska T (1992) Cellular neural networks with nonlinear and delay type template elements and non-uniform grids. Int J Circuit Theory Appl 20:449–451CrossRefMATH
2.
Zurück zum Zitat Civalleri PP, Gilli M, Pandolfi L (1993) On stability of cellular neural networks with delay. IEEE Trans Circuits Syst I Fundam Theory Appl 40:157–164CrossRefMATH Civalleri PP, Gilli M, Pandolfi L (1993) On stability of cellular neural networks with delay. IEEE Trans Circuits Syst I Fundam Theory Appl 40:157–164CrossRefMATH
3.
Zurück zum Zitat Hopfield JJ (1984) Neurons with graded response have collective computational properties like those of two-stage neurons. Proc Natl Acad Sci Biol 81:3088–3092CrossRefMATH Hopfield JJ (1984) Neurons with graded response have collective computational properties like those of two-stage neurons. Proc Natl Acad Sci Biol 81:3088–3092CrossRefMATH
4.
Zurück zum Zitat Bouzerdoum A, Pattison T (1993) Neural networks for quadratic optimization with bound constraints. IEEE Trans Neural Netw 4:293–303CrossRef Bouzerdoum A, Pattison T (1993) Neural networks for quadratic optimization with bound constraints. IEEE Trans Neural Netw 4:293–303CrossRef
5.
Zurück zum Zitat Xie W, Zhu Q (2015) Mean square exponential stability of stochastic fuzzy delayed Cohen–Grossberg neural networks with expectations in the coefficients. Neurocomputing 166:133–139CrossRef Xie W, Zhu Q (2015) Mean square exponential stability of stochastic fuzzy delayed Cohen–Grossberg neural networks with expectations in the coefficients. Neurocomputing 166:133–139CrossRef
6.
Zurück zum Zitat Liu L, Zhu Q (2015) Almost sure exponential stability of numerical solutions to stochastic delay Hopfield neural networks. Appl Math Comput 266:698–712MathSciNet Liu L, Zhu Q (2015) Almost sure exponential stability of numerical solutions to stochastic delay Hopfield neural networks. Appl Math Comput 266:698–712MathSciNet
7.
Zurück zum Zitat Zhu Q, Cao J, Rakkiyappan R (2015) Exponential input-to-state stability of stochastic Cohen–Grossberg neural networks with mixed delays. Nonlinear Dyn 79:1085–1098MathSciNetCrossRefMATH Zhu Q, Cao J, Rakkiyappan R (2015) Exponential input-to-state stability of stochastic Cohen–Grossberg neural networks with mixed delays. Nonlinear Dyn 79:1085–1098MathSciNetCrossRefMATH
8.
Zurück zum Zitat Tang Y, Gao H, Zhang W, Kurths J (2015) Leader-following consensus of a class of stochastic delayed multi-agent systems with partial mixed impulses. Automatica 53:346–354MathSciNetCrossRefMATH Tang Y, Gao H, Zhang W, Kurths J (2015) Leader-following consensus of a class of stochastic delayed multi-agent systems with partial mixed impulses. Automatica 53:346–354MathSciNetCrossRefMATH
9.
Zurück zum Zitat Yang R, Wu B, Liu Y (2015) A Halanay-type inequality approach to the stability analysis of discrete-time neural networks with delays. Appl Math Comput 265:696–707MathSciNet Yang R, Wu B, Liu Y (2015) A Halanay-type inequality approach to the stability analysis of discrete-time neural networks with delays. Appl Math Comput 265:696–707MathSciNet
10.
Zurück zum Zitat Wu B, Liu Y, Lu J (2012) New results on global exponential stability for impulsive cellular neural networks with any bounded time-varying delays. Math Comput Modell 55:837–843MathSciNetCrossRefMATH Wu B, Liu Y, Lu J (2012) New results on global exponential stability for impulsive cellular neural networks with any bounded time-varying delays. Math Comput Modell 55:837–843MathSciNetCrossRefMATH
11.
Zurück zum Zitat Zhang W, Tang Y, Wu X, Fang JA (2014) Synchronization of nonlinear dynamical networks with heterogeneous impulses. IEEE Trans Circuits Syst I 61:1220–1228CrossRef Zhang W, Tang Y, Wu X, Fang JA (2014) Synchronization of nonlinear dynamical networks with heterogeneous impulses. IEEE Trans Circuits Syst I 61:1220–1228CrossRef
12.
Zurück zum Zitat Zhang W, Tang Y, Miao Q, Du W (2013) Exponential synchronization of coupled switched neural networks with mode-dependent impulsive effects. IEEE Trans Neural Netw Learn Syst 24:1316–1326CrossRef Zhang W, Tang Y, Miao Q, Du W (2013) Exponential synchronization of coupled switched neural networks with mode-dependent impulsive effects. IEEE Trans Neural Netw Learn Syst 24:1316–1326CrossRef
13.
Zurück zum Zitat Liu Y, Chen H, Wu B (2014) Controllability of Boolean control networks with impulsive effects and forbidden states. Math Methods Appl Sci 37:1–9MathSciNetCrossRefMATH Liu Y, Chen H, Wu B (2014) Controllability of Boolean control networks with impulsive effects and forbidden states. Math Methods Appl Sci 37:1–9MathSciNetCrossRefMATH
14.
Zurück zum Zitat Liu Y, Cao J, Sun L, Lu J (2016) Sampled-data state feedback stabilization of boolean control networks. Neural Comput 28:1–22CrossRef Liu Y, Cao J, Sun L, Lu J (2016) Sampled-data state feedback stabilization of boolean control networks. Neural Comput 28:1–22CrossRef
15.
Zurück zum Zitat Shah S, Wiener J (1983) Advanced differential equations with piecewise constant argument deviations. Int J Math Sci 6:671–703MathSciNetCrossRefMATH Shah S, Wiener J (1983) Advanced differential equations with piecewise constant argument deviations. Int J Math Sci 6:671–703MathSciNetCrossRefMATH
16.
17.
Zurück zum Zitat Wiener J (1993) Generalized solutions of functional differential equations. WorldScientific, SingaporeCrossRefMATH Wiener J (1993) Generalized solutions of functional differential equations. WorldScientific, SingaporeCrossRefMATH
18.
Zurück zum Zitat Bereketoglu H, Seyhan G, Ogun A (2010) Advanced impulsive differential equations with piecewise constant arguments. Math Model Anal 15:175–187MathSciNetCrossRefMATH Bereketoglu H, Seyhan G, Ogun A (2010) Advanced impulsive differential equations with piecewise constant arguments. Math Model Anal 15:175–187MathSciNetCrossRefMATH
19.
Zurück zum Zitat Abbas S, Xia Y (2015) Almost automorphic solutions of impulsive cellular neural networks with piecewise constant argument. Neural Process Lett 42:691–702CrossRef Abbas S, Xia Y (2015) Almost automorphic solutions of impulsive cellular neural networks with piecewise constant argument. Neural Process Lett 42:691–702CrossRef
20.
Zurück zum Zitat Muroya Y (2008) New contractivity condition in a population model with piecewise constant arguments. J Math Anal Appl 346:65–81MathSciNetCrossRefMATH Muroya Y (2008) New contractivity condition in a population model with piecewise constant arguments. J Math Anal Appl 346:65–81MathSciNetCrossRefMATH
21.
Zurück zum Zitat Akhmet MU, Aruğaslan D, Yılmaz E (2010) Stability analysis of recurrent neural networks with piecewise constant argument of generalized type. Neural Netw 23:805–811CrossRefMATH Akhmet MU, Aruğaslan D, Yılmaz E (2010) Stability analysis of recurrent neural networks with piecewise constant argument of generalized type. Neural Netw 23:805–811CrossRefMATH
22.
Zurück zum Zitat Akhmet MU, Büyükadali C (2008) On periodic solutions of differential equations with piecewise constant argument. Comput Math Appl 56:2034–2042MathSciNetCrossRefMATH Akhmet MU, Büyükadali C (2008) On periodic solutions of differential equations with piecewise constant argument. Comput Math Appl 56:2034–2042MathSciNetCrossRefMATH
23.
Zurück zum Zitat Akhmet MU, Yılmaz E (2010) Impulsive Hopfield-type neural networks system with piecewise constant argument. Nonlinear Anal Real World Appl 11:2584–2593MathSciNetCrossRefMATH Akhmet MU, Yılmaz E (2010) Impulsive Hopfield-type neural networks system with piecewise constant argument. Nonlinear Anal Real World Appl 11:2584–2593MathSciNetCrossRefMATH
24.
Zurück zum Zitat Akhmet MU, Yilmaz R (2012) Global exponential stability of neural networks with non-smooth and impact activations. Neural Netw 34:18–27CrossRefMATH Akhmet MU, Yilmaz R (2012) Global exponential stability of neural networks with non-smooth and impact activations. Neural Netw 34:18–27CrossRefMATH
25.
Zurück zum Zitat Bao G, Wen S, Zeng Z (2012) Robust stability analysis of interval fuzzy Cohen–Grossberg neural networks with piecewise constant argument of generalized type. Neural Netw 33:32–41CrossRefMATH Bao G, Wen S, Zeng Z (2012) Robust stability analysis of interval fuzzy Cohen–Grossberg neural networks with piecewise constant argument of generalized type. Neural Netw 33:32–41CrossRefMATH
26.
Zurück zum Zitat Chiu KS (2013) Existence and global exponential stability of equilibrium for impulsive cellular neural networks models with piecewise alternately advanced and retarded argument. Abstr Appl Anal. doi:10.1155/2013/196139 MathSciNetMATH Chiu KS (2013) Existence and global exponential stability of equilibrium for impulsive cellular neural networks models with piecewise alternately advanced and retarded argument. Abstr Appl Anal. doi:10.​1155/​2013/​196139 MathSciNetMATH
27.
Zurück zum Zitat Xi Q (2016) Global exponential stability of Cohen–Grossberg neural networks with piecewise constant argument of generalized type and impulses. IEEE Neural Comput 28:229–255CrossRef Xi Q (2016) Global exponential stability of Cohen–Grossberg neural networks with piecewise constant argument of generalized type and impulses. IEEE Neural Comput 28:229–255CrossRef
28.
Zurück zum Zitat Xu DY, Yang ZC (2006) Existence and exponential stability of periodic solution in impulsive delay differential equations and application. Nonlinear Anal Theory Methods Appl 64:130–145CrossRefMATH Xu DY, Yang ZC (2006) Existence and exponential stability of periodic solution in impulsive delay differential equations and application. Nonlinear Anal Theory Methods Appl 64:130–145CrossRefMATH
29.
Zurück zum Zitat Li XD (2009) Global exponential stability of Cohen–Grossberg-type BAM neural networks with time-varying delays via impulsive control. Neurocomputing 73:525–530CrossRef Li XD (2009) Global exponential stability of Cohen–Grossberg-type BAM neural networks with time-varying delays via impulsive control. Neurocomputing 73:525–530CrossRef
30.
Zurück zum Zitat Yu T, Cao D, Liu S, Chen H (2016) Stability analysis of neural networks with periodic coefficients and piecewise constant arguments. J Franklin Inst 353:409–425MathSciNetCrossRef Yu T, Cao D, Liu S, Chen H (2016) Stability analysis of neural networks with periodic coefficients and piecewise constant arguments. J Franklin Inst 353:409–425MathSciNetCrossRef
31.
Zurück zum Zitat Ballinger G, Liu X (1999) Existence and uniqueness results for impulsive delay differential equations. Dyn Contin Discret Impuls Syst 5:579–591MathSciNetMATH Ballinger G, Liu X (1999) Existence and uniqueness results for impulsive delay differential equations. Dyn Contin Discret Impuls Syst 5:579–591MathSciNetMATH
32.
Zurück zum Zitat Alwan MS, Liu XZ, Xie WC (2013) Comparison principle and stability of differential equations with piecewise constant arguments. J Franklin Inst 350:211–230MathSciNetCrossRefMATH Alwan MS, Liu XZ, Xie WC (2013) Comparison principle and stability of differential equations with piecewise constant arguments. J Franklin Inst 350:211–230MathSciNetCrossRefMATH
Metadaten
Titel
Stability Analysis of Impulsive Neural Networks with Piecewise Constant Arguments
verfasst von
Tianhu Yu
Dengqing Cao
Publikationsdatum
02.06.2017
Verlag
Springer US
Erschienen in
Neural Processing Letters / Ausgabe 1/2018
Print ISSN: 1370-4621
Elektronische ISSN: 1573-773X
DOI
https://doi.org/10.1007/s11063-017-9638-y

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