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Neural Processing Letters

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02-06-2017

Stability Analysis of Impulsive Neural Networks with Piecewise Constant Arguments

Authors: Tianhu Yu, Dengqing Cao

Published in: Neural Processing Letters | Issue 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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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

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

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

Bouzerdoum A, Pattison T (1993) Neural networks for quadratic optimization with bound constraints. IEEE Trans Neural Netw 4:293–303CrossRef

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

Liu L, Zhu Q (2015) Almost sure exponential stability of numerical solutions to stochastic delay Hopfield neural networks. Appl Math Comput 266:698–712MathSciNet

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

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

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.

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.

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.

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.

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.

Liu Y, Cao J, Sun L, Lu J (2016) Sampled-data state feedback stabilization of boolean control networks. Neural Comput 28:1–22CrossRef

15.

Shah S, Wiener J (1983) Advanced differential equations with piecewise constant argument deviations. Int J Math Sci 6:671–703MathSciNetCrossRefMATH

16.

Cooke K, Wiener J (1984) Retarded differential equations with piecewise constant delays. J Math Anal Appl 99:265–297MathSciNetCrossRefMATH

17.

Wiener J (1993) Generalized solutions of functional differential equations. WorldScientific, SingaporeCrossRefMATH

18.

Bereketoglu H, Seyhan G, Ogun A (2010) Advanced impulsive differential equations with piecewise constant arguments. Math Model Anal 15:175–187MathSciNetCrossRefMATH

19.

Abbas S, Xia Y (2015) Almost automorphic solutions of impulsive cellular neural networks with piecewise constant argument. Neural Process Lett 42:691–702CrossRef

20.

Muroya Y (2008) New contractivity condition in a population model with piecewise constant arguments. J Math Anal Appl 346:65–81MathSciNetCrossRefMATH

21.

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.

Akhmet MU, Büyükadali C (2008) On periodic solutions of differential equations with piecewise constant argument. Comput Math Appl 56:2034–2042MathSciNetCrossRefMATH

23.

Akhmet MU, Yılmaz E (2010) Impulsive Hopfield-type neural networks system with piecewise constant argument. Nonlinear Anal Real World Appl 11:2584–2593MathSciNetCrossRefMATH

24.

Akhmet MU, Yilmaz R (2012) Global exponential stability of neural networks with non-smooth and impact activations. Neural Netw 34:18–27CrossRefMATH

25.

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.

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.

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.

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.

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.

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.

Ballinger G, Liu X (1999) Existence and uniqueness results for impulsive delay differential equations. Dyn Contin Discret Impuls Syst 5:579–591MathSciNetMATH

32.

Alwan MS, Liu XZ, Xie WC (2013) Comparison principle and stability of differential equations with piecewise constant arguments. J Franklin Inst 350:211–230MathSciNetCrossRefMATH

Title: Stability Analysis of Impulsive Neural Networks with Piecewise Constant Arguments
Authors: Tianhu Yu
Dengqing Cao
Publication date: 02-06-2017
Publisher: Springer US
Published in: Neural Processing Letters / Issue 1/2018
Print ISSN: 1370-4621
Electronic ISSN: 1573-773X
DOI: https://doi.org/10.1007/s11063-017-9638-y

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