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Neural Computing and Applications
Published in: Neural Computing and Applications 9/2019

09-03-2018 | Original Article

Piecewise asymptotically almost automorphic solutions for impulsive non-autonomous high-order Hopfield neural networks with mixed delays

Authors: Chaouki Aouiti, Farah Dridi

Published in: Neural Computing and Applications | Issue 9/2019

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Abstract

This paper is concerned with an impulsive non-autonomous high-order Hopfield neural network with mixed delays. Under proper conditions, we studied the existence, the uniqueness and the global exponential stability of asymptotic almost automorphic solutions for the suggested system. Our method was mainly based on the Banach’s fixed-point theorem and the generalized Gronwall–Bellman inequality. Moreover, four examples are presented to demonstrate the effectiveness of the proposed findings.
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Appendix
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Literature
1.
Abbas S, Mahto L, Hafayed M, Alimi AM (2014) Asymptotic almost automorphic solutions of impulsive neural network with almost automorphic coefficients. Neurocomputing 142:326–33CrossRef
2.
Abbas S, Kavitha V, Murugesu R (2015) Stepanov-like weighted pseudo almost automorphic solutions to fractional order abstract integro-differential equations. Proc Math Sci 125(3):323–351MathSciNetMATHCrossRef
3.
Abbas S, Chang YK, Hafayed M (2014) Stepanov type weighted pseudo almost automorphic sequences and their applications to difference equations. Nonlinear Stud 21(1):99–111MathSciNetMATH
4.
Abbas S, Yonghui XIA (2013) Existence and attractivity of k-almost automorphic sequence solution of a model of cellular neural networks with delay. Acta Math Sci 33(1):290–302MathSciNetMATHCrossRef
5.
Abbas S, Xia Y (2015) Almost automorphic solutions of impulsive cellular neural networks with piecewise constant argument. Neural Process Lett 42(3):691–702CrossRef
6.
Ammar B, Chérif F, Alimi AM (2012) Existence and uniqueness of pseudo almost-periodic solutions of recurrent neural networks with time-varying coefficients and mixed delays. IEEE Trans Neural Netw Learn Syst 23(1):109–118CrossRef
7.
Aouiti C, M’hamdi MS, Touati A (2017) Pseudo almost automorphic solutions of recurrent neural networks with time-varying coefficients and mixed delays. Neural Process Lett 45(1):121–140CrossRef
8.
Aouiti C, M’hamdi MS, Cao J, Alsaedi A (2017) Piecewise pseudo almost periodic solution for impulsive generalised high-order Hopfield neural networks with leakage delays. Neural Process Lett 45(2):615–648CrossRef
9.
10.
Aouiti C (2016) Neutral impulsive shunting inhibitory cellular neural networks with time-varying coefficients and leakage delays. Cogn Neurodyn 10(6):573–591MathSciNetCrossRef
11.
Aouiti C, M’hamdi MS, Chérif F (2017) New results for impulsive recurrent neural networks with time-varying coefficients and mixed delays. Neural Process Lett 46(2):487–506CrossRef
12.
Aouiti C, Coirault P, Miaadi F, Moulay E (2017) Finite time boundedness of neutral high-order Hopfield neural networks with time delay in the leakage term and mixed time delays. Neurocomputing 260:378–392CrossRef
13.
14.
Brahmi H, Ammar B, Chérif F, Alimi AM (2014) On the dynamics of the high-order type of neural networks with time varying coefficients and mixed delay. In: 2014 international joint conference on neural networks (IJCNN), pp 2063–2070
15.
Brahmi H, Ammar B, Chérif F, Alimi AM, Abraham A (2016) Asymptotically almost automorphic solution of high order recurrent neural networks with mixed delays. Int J Comput Sci Inf Secur 14(7):284
16.
Brahmi H, Ammar B, Alimi AM, Chérif F (2016) Pseudo almost periodic solutions of impulsive recurrent neural networks with mixed delays. In: 2016 international joint conference on neural networks (IJCNN), pp 464–470. IEEE
17.
Cai SM, Xu FD, Zheng WX, Liu ZR (2009) Exponential stability analysis for impulsive neural networks with time-varying delays. In: Optimization and systems biology: the third international symposium, OSB’09, Zhangjiajie, China, 20–22 Sept 2009. Proceedings, pp 81–88
18.
Cao J, Wang L (2002) Exponential stability and periodic oscillatory solution in BAM networks with delays. IEEE Trans Neural Netw 13(2):457–463CrossRef
19.
Cao J (2003) New results concerning exponential stability and periodic solutions of delayed cellular neural networks. Phys Lett A 307(2):136–147MathSciNetMATHCrossRef
20.
Cao J, Wang J (2005) Global asymptotic and robust stability of recurrent neural networks with time delays. IEEE Trans Circuits Syst I Regul Pap 52(2):417–426MathSciNetMATHCrossRef
21.
Cao J, Liang J, Lam J (2004) Exponential stability of high-order bidirectional associative memory neural networks with time delays. Phys D Nonlinear Phenom 199(3):425–436MathSciNetMATHCrossRef
22.
Cao J, Chen A, Huang X (2005) Almost periodic attractor of delayed neural networks with variable coefficients. Phys Lett A 340(1):104–120MATHCrossRef
23.
Cao J, Song Q (2006) Stability in Cohen–Grossberg-type bidirectional associative memory neural networks with time-varying delays. Nonlinearity 19(7):1601–1617MathSciNetMATHCrossRef
24.
Chang YK, Cheng ZX, N’Guérékata GM (2016) Stepanov-like pseudo almost automorphic solutions to some stochastic differential equations. Bull Malays Math Sci Soc 39(1):181–197MathSciNetMATHCrossRef
25.
Chang YK, Luo XX (2015) Pseudo almost automorphic behavior of solutions to a semi-linear fractional differential equation. Math Commun 20(1):53–68MathSciNetMATH
26.
Chang YK, Bian YT (2015) Weighted asymptotic behavior of solutions to a Sobolev-type differential equation with Stepanov coefficients in Banach spaces. Filomat 29(6):1315–1328MathSciNetMATHCrossRef
27.
Chang YK, Zhang R, N’Guérékata GM (2014) Weighted pseudo almost automorphic solutions to nonautonomous semilinear evolution equations with delay and ${S}^{p} $-weighted pseudo almost automorphic coefficients. Topol Methods Nonlinear Anal 43(1):69–88MathSciNetMATHCrossRef
28.
Chang YK, Luo XX (2014) Existence of $\mu $-pseudo almost automorphic solutions to a neutral differential equation by interpolation theory. Filomat 28(3):603–614MathSciNetMATHCrossRef
29.
Chavez A, Castillo S, Pinto M (2013) Discontinuous almost automorphic functions and almost automorphic solutions of differential equations with piecewise constant argument. Electron J Differ Equ 56:113MATH
30.
Chen A, Cao J (2003) Existence and attractivity of almost periodic solutions for cellular neural networks with distributed delays and variable coefficients. Appl Math Comput 134(1):125–140MathSciNetMATH
31.
Chérif F (2014) Sufficient conditions for global stability and existence of almost automorphic solution of a class of RNNs. Differ Equ Dyn Syst 22(2):191–207MathSciNetMATHCrossRef
32.
Diagana T (2013) Almost automorphic type and almost periodic type functions in abstract spaces. Springer, New YorkMATHCrossRef
33.
Gerlee P, Anderson AR (2009) Modelling evolutionary cell behaviour using neural networks: application to tumour growth. Biosystems 95(2):166–174CrossRef
34.
Huang X, Cao J, Ho DW (2006) Existence and attractivity of almost periodic solution for recurrent neural networks with unbounded delays and variable coefficients. Nonlinear Dyn 45(3):337–351MathSciNetMATHCrossRef
35.
Kavitha V, Abbas S, Murugesu R (2015) Asymptotically almost automorphic solutions of fractional order neutral integro-differential equations. Bull Malays Math Sci Soc 39(3):1075–1088MathSciNetMATHCrossRef
36.
Kavitha V, Wang PZ, Murugesu R (2013) Existence of weighted pseudo almost automorphic mild solutions to fractional integro-differential equations. J Fract Calc Appl 4(1):37–55
37.
Li Y (2013) Periodic solutions of non-autonomous cellular neural networks with impulses and delays on time scales. IMA J Math Control Inf 31(2):273–293MathSciNetMATHCrossRef
38.
Liang J, Zhang J, Xiao TJ (2008) Composition of pseudo almost automorphic and asymptotically almost automorphic functions. J Math Anal Appl 340(2):1493–1499MathSciNetMATHCrossRef
39.
M’hamdi MS, Aouiti C, Touati A, Alimi AM, Snasel V (2016) Weighted pseudo almost-periodic solutions of shunting inhibitory cellular neural networks with mixed delays. Acta Math Sci 36(6):1662–1682MathSciNetMATHCrossRef
40.
Mahto L, Abbas S (2015) PC-almost automorphic solution of impulsive fractional differential equations. Mediterr J Math 12(3):771–790MathSciNetMATHCrossRef
41.
Marcus CM, Westervelt RM (1988) Dynamics of analog neural networks with time delay. In: NIPS, pp 568–576
42.
43.
Moghtadaei M, Golpayegani MRH, Malekzadeh R (2013) A variable structure fuzzy neural network model of squamous dysplasia and esophageal squamous cell carcinoma based on a global chaotic optimization algorithm. J Theor Biol 318:164–172MathSciNetMATHCrossRef
44.
45.
Mohamad S, Gopalsamy K, Akca H (2008) Exponential stability of artificial neural networks with distributed delays and large impulses. Nonlinear Anal Real World Appl 9(3):872–888MathSciNetMATHCrossRef
46.
N’Guérékata GM (1981) Sur les solutions presque automorphes d’équations différentielles abstraites. Ann Sci Math Quebec 5(1):69–79MathSciNetMATH
47.
N’Guérékata GM (1987) Some remarks on asymptotically almost automorphic functions. Riv Math Universita di Parma 13(4):301–303MathSciNetMATH
48.
Rakkiyappan R, Pradeep C, Vinodkumar A, Rihan FA (2013) Dynamic analysis for high-order Hopfield neural networks with leakage delay and impulsive effects. Neural Comput Appl 22(1):55–73CrossRef
49.
Ren F, Cao J (2006) LMI-based criteria for stability of high-order neural networks with time-varying delay. Nonlinear Anal Real World Appl 7(5):967–979MathSciNetMATHCrossRef
50.
Ren F, Cao J (2007) Periodic oscillation of higher-order bidirectional associative memory neural networks with periodic coefficients and delays. Nonlinearity 20(3):605–629MathSciNetMATHCrossRef
51.
Ren F, Cao J (2007) Periodic solutions for a class of higher-order Cohen–Grossberg type neural networks with delays. Comput Math Appl 54(6):826–839MathSciNetMATHCrossRef
52.
Stamov GT (2012) Almost periodic solutions of impulsive differential equations. Springer, BerlinMATHCrossRef
53.
54.
Shi P, Dong L (2010) Existence and exponential stability of anti-periodic solutions of Hopfield neural networks with impulses. Appl Math Comput 216(2):623–630MathSciNetMATH
55.
Tonnesen J (2013) Optogenetic cell control in experimental models of neurological disorders. Behav Brain Res 255:35–43CrossRef
56.
Tyagi S, Abbas S, Hafayed M (2016) Global Mittag–Leffler stability of complex valued fractional-order neural network with discrete and distributed delays. Rendiconti del Circolo Matematico di Palermo Series 2 65(3):485–505MathSciNetMATHCrossRef
57.
Wang C (2016) Piecewise pseudo almost periodic solution for impulsive non-autonomous high-order Hopfield neural networks with variable delays. Neurocomputing 171:1291–1301CrossRef
58.
Wang C, Agarwal RP (2015) Weighted piecewise pseudo almost automorphic functions with applications to abstract impulsive $\nabla $-dynamic equations on time scales. Adv Differ Equ 2014(1):153MATHCrossRef
59.
Wang J, Jiang H, Hu C (2014) Existence and stability of periodic solutions of discrete-time Cohen–Grossberg neural networks with delays and impulses. Neurocomputing 142:542–550CrossRef
60.
Wang Y, Xiong W, Zhou Q, Xiao B, Yu Y (2006) Global exponential stability of cellular neural networks with continuously distributed delays and impulses. Phys Lett A 350(1):89–95MATHCrossRef
61.
Weng YF, Ju L, Wang J (2007) Cellular neural networks and biological visual information processing model. J Beijing Technol Bus Univ (Nat Sci Ed) 25(1):42–58
62.
Xiong W (2015) New result on convergence for HCNNs with time-varying leakage delays. Neural Comput Appl 26(2):485–491CrossRef
63.
Xu C, Li P (2016) Pseudo almost periodic solutions for high-order Hopfield neural networks with time-varying leakage delays. Neural Process Lett 46(1):41–58CrossRef
64.
Xu B, Liu X, Teo KL (2009) Asymptotic stability of impulsive high-order Hopfield type neural networks. Comput Math Appl 57(11):1968–1977MathSciNetMATHCrossRef
65.
Xia Z (2016) Pseudo almost periodic mild solution of nonautonomous impulsive integro-differential equations. Mediterr J Math 13(3):1065–1086MathSciNetMATHCrossRef
66.
Yang Y, Cao J (2007) Stability and periodicity in delayed cellular neural networks with impulsive effects. Nonlinear Anal Real World Appl 8(1):362–374MathSciNetMATHCrossRef
67.
Yang X, Cao J, Huang C, Long Y (2010) Existence and global exponential stability of almost periodic solutions for SICNNs with nonlinear behaved functions and mixed delays. In: Abstract and applied analysis. Hindawi Publishing Corporation
68.
Zhang Q, Wei X, Xu J (2003) Global exponential stability of Hopfield neural networks with continuously distributed delays. Phys Lett A 315(6):431–436MathSciNetMATHCrossRef
69.
Zhu Q, Liang F, Zhang Q (2009) Global exponential stability of Cohen-Grossberg neural networks with time-varying delays and impulses. J Shanghai Univ (Engl Ed) 13(3):255–259MathSciNetMATHCrossRef
Metadata
Title
Piecewise asymptotically almost automorphic solutions for impulsive non-autonomous high-order Hopfield neural networks with mixed delays
Authors
Chaouki Aouiti
Farah Dridi
Publication date
09-03-2018
Publisher
Springer London
Published in
Neural Computing and Applications / Issue 9/2019
Print ISSN: 0941-0643
Electronic ISSN: 1433-3058
DOI
https://doi.org/10.1007/s00521-018-3378-4

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