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Published in: Neural Processing Letters 2/2017

22-06-2016

Global Exponential Convergence of Neutral Type Shunting Inhibitory Cellular Neural Networks with D Operator

Author: Luogen Yao

Published in: Neural Processing Letters | Issue 2/2017

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Abstract

In this paper, a class of neutral type shunting inhibitory cellular neural networks with D operator are considered. Several novel conditions which guarantee the global exponential convergence of considered models are established by using Lyapunov functional method and differential inequality techniques. Moreover, an example and its numerical simulations are given to show the effectiveness of the obtained results.

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Literature
2.
go back to reference Komanovskii VB, Nosov VR (1986) Stability of functional differential equations. Academic Press, London Komanovskii VB, Nosov VR (1986) Stability of functional differential equations. Academic Press, London
3.
go back to reference Kuang Y (1993) Delay differential equations with applications in population dynamical system. Academic Press, New YorkMATH Kuang Y (1993) Delay differential equations with applications in population dynamical system. Academic Press, New YorkMATH
4.
go back to reference Chen Z (2013) A shunting inhibitory cellular neural network with leakage delays and continuously distributed delays of neutral type. Neural Comput Appl 23:2429–2434CrossRef Chen Z (2013) A shunting inhibitory cellular neural network with leakage delays and continuously distributed delays of neutral type. Neural Comput Appl 23:2429–2434CrossRef
5.
go back to reference Liu X (2015) Exponential convergence of SICNNs with delays and oscillating coefficients in leakage terms. Neurocomputing 168:500–504CrossRef Liu X (2015) Exponential convergence of SICNNs with delays and oscillating coefficients in leakage terms. Neurocomputing 168:500–504CrossRef
6.
go back to reference Zhao C, Wang Z (2015) Exponential convergence of a SICNN with leakage delays and continuously distributed delays of neutral type. Neural Process Lett 41:239–247CrossRef Zhao C, Wang Z (2015) Exponential convergence of a SICNN with leakage delays and continuously distributed delays of neutral type. Neural Process Lett 41:239–247CrossRef
7.
go back to reference Gui Z, Ge W, Yang X (2007) Periodic oscillation for a Hopfield neural networks with neutral delays. Phys Lett A 364(3–4):267–273CrossRefMATH Gui Z, Ge W, Yang X (2007) Periodic oscillation for a Hopfield neural networks with neutral delays. Phys Lett A 364(3–4):267–273CrossRefMATH
8.
go back to reference Xiao B (2009) Existence and uniqueness of almost periodic solutions for a class of Hopfield neural networks with neutral delays. Appl Math Lett 22:528–533MathSciNetCrossRefMATH Xiao B (2009) Existence and uniqueness of almost periodic solutions for a class of Hopfield neural networks with neutral delays. Appl Math Lett 22:528–533MathSciNetCrossRefMATH
9.
go back to reference Mandal S, Majee NC (2011) Existence of periodic solutions for a class of Cohen-Grossberg type neural networks with neutral delays. Neurocomputing 74(6):1000–1007CrossRef Mandal S, Majee NC (2011) Existence of periodic solutions for a class of Cohen-Grossberg type neural networks with neutral delays. Neurocomputing 74(6):1000–1007CrossRef
10.
go back to reference Liu B (2015) Pseudo almost periodic solutions for neutral type CNNs with continuously distributed leakage delays. Neurocomputing 148:445–454CrossRef Liu B (2015) Pseudo almost periodic solutions for neutral type CNNs with continuously distributed leakage delays. Neurocomputing 148:445–454CrossRef
11.
12.
go back to reference Liu B, Huang L (2006) Existence and uniqueness of periodic solutions for a kind of first order neutral functional differential equations. J Math Anal Appl 322(1):121–132MathSciNetCrossRefMATH Liu B, Huang L (2006) Existence and uniqueness of periodic solutions for a kind of first order neutral functional differential equations. J Math Anal Appl 322(1):121–132MathSciNetCrossRefMATH
13.
go back to reference Liu B, Huang L (2007) Existence and uniqueness of periodic solutions for a kind of first order neutral functional differential equations with a deviating argument. Taiwan J Math 11(2):497–510MathSciNetMATH Liu B, Huang L (2007) Existence and uniqueness of periodic solutions for a kind of first order neutral functional differential equations with a deviating argument. Taiwan J Math 11(2):497–510MathSciNetMATH
14.
go back to reference Peng L, Wang L (2014) Periodic solutions for first order neutral functional differential equations with multiple deviating arguments. Ann Polon Math 111(2):197–213MathSciNetCrossRefMATH Peng L, Wang L (2014) Periodic solutions for first order neutral functional differential equations with multiple deviating arguments. Ann Polon Math 111(2):197–213MathSciNetCrossRefMATH
15.
go back to reference Luo Y, Wang W, Shen J (2008) Existence of positive periodic solutions for two kinds of neutral functional differential equations. Appl Math Lett 21:581–587MathSciNetCrossRefMATH Luo Y, Wang W, Shen J (2008) Existence of positive periodic solutions for two kinds of neutral functional differential equations. Appl Math Lett 21:581–587MathSciNetCrossRefMATH
16.
go back to reference Candan T (2016) Existence of positive periodic solutions of first order neutral differential equations with variable coefficients. Appl Math Lett 52:142–148MathSciNetCrossRefMATH Candan T (2016) Existence of positive periodic solutions of first order neutral differential equations with variable coefficients. Appl Math Lett 52:142–148MathSciNetCrossRefMATH
17.
go back to reference Jiang A (2015) Exponential convergence for shunting inhibitory cellular neural networks with oscillating coefficients in leakage terms. Neurocomputing 165:159–162CrossRef Jiang A (2015) Exponential convergence for shunting inhibitory cellular neural networks with oscillating coefficients in leakage terms. Neurocomputing 165:159–162CrossRef
18.
go back to reference Jiang A (2016) Exponential convergence for HCNNs with oscillating coefficients in leakage terms. Neural Process Lett 43:285–294CrossRef Jiang A (2016) Exponential convergence for HCNNs with oscillating coefficients in leakage terms. Neural Process Lett 43:285–294CrossRef
19.
go back to reference Zhang H, Liu X, Yang M (2015) Global exponential stability of a delay reduced SIR model for migrant workers’ home residence. Appl Math Lett 50:119–125MathSciNetCrossRefMATH Zhang H, Liu X, Yang M (2015) Global exponential stability of a delay reduced SIR model for migrant workers’ home residence. Appl Math Lett 50:119–125MathSciNetCrossRefMATH
20.
go back to reference Long Z (2016) New results on anti-periodic solutions for SICNNs with oscillating coefficients in leakage terms. Neurocomputing 171(1):503–509CrossRef Long Z (2016) New results on anti-periodic solutions for SICNNs with oscillating coefficients in leakage terms. Neurocomputing 171(1):503–509CrossRef
21.
go back to reference Liu X (2016) Improved convergence criteria for HCNNs with delays and oscillating coefficients in leakage terms. Neural Comput Appl 27:917–925CrossRef Liu X (2016) Improved convergence criteria for HCNNs with delays and oscillating coefficients in leakage terms. Neural Comput Appl 27:917–925CrossRef
22.
go back to reference Liu B (2016) Global exponential convergence of non-autonomous cellular neural networks with multi-proportional delays. Neurocomputing 191:352–355 Liu B (2016) Global exponential convergence of non-autonomous cellular neural networks with multi-proportional delays. Neurocomputing 191:352–355
24.
go back to reference Yu Y (2016) Global exponential convergence for a class of neutral functional differential equations with proportional delays. Math Methods Appl Sci. doi:10.1002/mma.3880 Yu Y (2016) Global exponential convergence for a class of neutral functional differential equations with proportional delays. Math Methods Appl Sci. doi:10.​1002/​mma.​3880
25.
go back to reference Yu Y (2016) Global exponential convergence for a class of HCNNs with neutral time-proportional delays. Appl Math Comput 285:1–7MathSciNet Yu Y (2016) Global exponential convergence for a class of HCNNs with neutral time-proportional delays. Appl Math Comput 285:1–7MathSciNet
Metadata
Title
Global Exponential Convergence of Neutral Type Shunting Inhibitory Cellular Neural Networks with D Operator
Author
Luogen Yao
Publication date
22-06-2016
Publisher
Springer US
Published in
Neural Processing Letters / Issue 2/2017
Print ISSN: 1370-4621
Electronic ISSN: 1573-773X
DOI
https://doi.org/10.1007/s11063-016-9529-7

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