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International Journal of Machine Learning and Cybernetics
Published in: International Journal of Machine Learning and Cybernetics 5/2019

18-12-2017 | Original Article

Global stability analysis of delayed complex-valued fractional-order coupled neural networks with nodes of different dimensions

Authors: Manchun Tan, Qi Pan

Published in: International Journal of Machine Learning and Cybernetics | Issue 5/2019

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Abstract

In this paper, the delayed fractional-order complex-valued coupled neural networks (FCCNNs) with nodes of different dimensions are investigated. Firstly, stability theorems for linear fractional-order systems with multiple delays are presented. Secondly, by using the homeomorphism theory, the existence and uniqueness of the equilibrium point for delayed FCCNNs are proved. Then, the global stability criteria for delayed FCCNNs are derived by comparison theorem. Finally, numerical examples are given to illustrate the effectiveness of the presented results.
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Literature
1.
Zhang HG, Wang ZS, Liu DR (2014) A comprehensive review of stability analysis of continuous-time recurrent neural networks. IEEE Trans Neural Netw Learn Syst 25(7):1229–1262CrossRef
2.
Chen H, Wu LY, Dou Q, Qin J, Li SL, Cheng JZ, Ni D, Heng PA (2017) Ultrasound standard plane detection using a composite neural network framework. IEEE Trans Cybern 47(6):1576–1586CrossRef
3.
Tong C, Li J, Zhu FM (2017) A convolutional neural network based method for event classification in event-driven multi-sensor network. Comput Electr Eng 60:90–99CrossRef
4.
Yu SQ, Jia D, Xu CY (2017) Convolutional neural networks for hyperspectral image classification. Neurocomputing 219:88–98CrossRef
5.
Tan MC, Zhang YN (2009) New sufficient conditions for global asymptotic stability of Cohen–Grossberg neural networks with time-varying delays. Nonlinear Anal Real World Appl 10(4):2139–2145MathSciNetCrossRefMATH
6.
Guo ZY, Wang J, Yan Z (2014) A systematic method for analyzing robust stability of interval neural networks with time-delays based on stability criteria. Neural Netw 54:112–122CrossRefMATH
7.
Zheng CD, Zhang HG, Wang ZS (2011) Novel exponential stability criteria of high-order neural networks with time-varying delays. IEEE Trans Syst Man Cybern B 41(2):486–496CrossRef
8.
Zheng CD, Zhang YL, Wang ZS (2016) Novel stability condition of stochastic fuzzy neural networks with Markovian jumping under impulsive perturbations. Int J Mach Learn Cybern 7(5):795–803CrossRef
9.
Feng JQ, Ma Q, Qin ST (2017) Exponential stability of periodic solution for impulsive memristor-based Cohen–Grossberg neural networks with mixed delays. Int J Pattern Recogn 31(7):1750022MathSciNetCrossRef
10.
Yang XS, Feng ZG, Feng JW, Cao JD (2017) Synchronization of discrete-time neural networks with delays and Markov jump topologies based on tracker information. Neural Netw 85:157–164CrossRef
11.
Wu CW, Chua LO (1995) Synchronization in an array of linearly coupled dynamical-systems. IEEE Trans Circuits Syst I 42(8):430–447MathSciNetCrossRefMATH
12.
Wu W, Chen TP (2008) Global synchronization criteria of linearly coupled neural network systems with time-varying coupling. IEEE Trans Neural Netw 19(2):319–332CrossRef
13.
Tseng JP (2013) Global asymptotic dynamics of a class of nonlinearly coupled neural networks with delays. Discrete Contin Dyn Syst 33(10):4693–4729MathSciNetCrossRefMATH
14.
Zhang HG, Gong DW, Chen B, Liu ZW (2013) Synchronization for coupled neural networks with interval delay: a novel augmented Lyapunov–Krasovskii functional method. IEEE Trans Neural Netw Learn Syst 24(1):58–70CrossRef
15.
Tan MC (2016) Stabilization of coupled time-delay neural networks with nodes of different dimensions. Neural Process Lett 43(1):255–268CrossRef
16.
Podlubny I (1999) Fractional differential equations. Academic Press, San DiegoMATH
17.
Morgado ML, Ford NJ, Lima PM (2013) Analysis and numerical methods for fractional differential equations with delay. J Comput Appl Math 252:159–168MathSciNetCrossRefMATH
18.
Gu YJ, Yu YG, Wang H (2016) Synchronization for fractional-order time-delayed memristor-based neural networks with parameter uncertainty. J Frankl Inst Eng Appl Math 353(15):3657–3684MathSciNetCrossRefMATH
19.
Wu AL, Liu L, Huang TW, Zeng ZG (2016) Mittag–Leffler stability of fractional-order neural networks in the presence of generalized piecewise constant arguments. Neural Netw 85:118–127CrossRef
20.
Wang H, Yu YG, Wen GG, Zhang S, Yu JZ (2015) Global stability analysis of fractional-order Hopfield neural networks with time delay. Neurocomputing 154:15–23CrossRef
21.
Zhang S, Yu YG, Hu W (2014) Robust stability analysis of fractional-order Hopfield neural networks with parameter uncertainties. Math Probl Eng 2014:302702MathSciNetMATH
22.
Yang XJ, Song QK, Liu YR, Zhao ZJ (2015) Finite-time stability analysis of fractional-order neural networks with delay. Neurocomputing 152:19–26CrossRef
23.
Chen BS, Chen JJ (2016) Global \(O(t^{-\alpha })\) image stability and global asymptotical periodicity for a non-autonomous fractional-order neural networks with time-varying delays. Neural Netw 73:47–57CrossRefMATH
24.
Wu AL, Liu L, Huang TW, Zeng ZG (2016) Mittag–Leffler stability of fractional-order neural networks in the presence of generalized piecewise constant arguments. Neural Netw 85:118–127CrossRef
25.
Chen LP, Liu C, Wu RC, He YG, Chai Y (2016) Finite-time stability criteria for a class of fractional-order neural networks with delay. Neural Comput Appl 27(3):549–556CrossRef
26.
Shao SY, Chen M, Yan XH (2016) Adaptive sliding mode synchronization for a class of fractional-order chaotic systems with disturbance. Nonlinear Dyn 83(4):1855–1866MathSciNetCrossRefMATH
27.
Hu J, Wang J (2012) Global stability of complex-valued recurrent neural networks with time-delays. IEEE Trans Neural Netw Learn Syst 23(6):853–865CrossRef
28.
Fang T, Sun JT (2014) Further investigate the stability of complex-valued recurrent neural networks with time-delays. IEEE Trans Neural Netw Learn Syst 25(9):1709–1713CrossRef
29.
Zhang ZQ, Yu SH (2016) Global asymptotic stability for a class of complex-valued Cohen–Grossberg neural networks with time delays. Neurocomputing 171:1158–1166CrossRef
30.
Wang ZY, Huang LH (2016) Global stability analysis for delayed complex-valued BAM neural networks. Neurocomputing 173:2083–2089CrossRef
31.
Liu XW, Chen TP (2016) Global exponential stability for complex-valued recurrent neural networks with asynchronous time delays. IEEE Trans Neural Netw Learn Syst 27(3):593–606MathSciNetCrossRef
32.
Alfaro-Ponce M, Salgado I, Arguelles A (2016) Adaptive identifier for uncertain complex-valued discrete-time nonlinear systems based on recurrent neural networks. Neural Process Lett 43(1):133–153CrossRef
33.
Zhou C, Zhang WL, Yang XS, Xu C, Feng JW (2017) Finite-time synchronization of complex-valued neural networks with mixed delays and uncertain perturbations. Neural Process Lett 46(1):271–291CrossRef
34.
Rakkiyappan R, Velmurugan G, Cao JD (2014) Finite-time stability analysis of fractional-order complex-valued memristor-based neural networks with time delays. Nonlinear Dyn 78(4):2823–2836MathSciNetCrossRefMATH
35.
Rakkiyappan R, Sivaranjani R, Velmurugan G (2016) Analysis of global \(O(t^{-\alpha })\) stability and global asymptotical periodicity for a class of fractional-order complex-valued neural networks with time varying delays. Neural Netw 77:51–69CrossRef
36.
Bao HB, Park JH, Cao JD (2016) Synchronization of fractional-order complex-valued neural networks with time delay. Neural Netw 81:16–28CrossRef
37.
Liu J (2014) Complex modified hybrid projective synchronization of different dimensional fractional-order complex chaos and real hyper-chaos. Entropy 16(12):6195–6211CrossRef
38.
Wu EL, Yang XS (2016) Adaptive synchronization of coupled nonidentical chaotic systems with complex variables and stochastic perturbations. Nonlinear Dyn 84(1):261–269MathSciNetCrossRefMATH
39.
Tan MC, Tian WX (2015) Finite-time stabilization and synchronization of complex dynamical networks with nonidentical nodes of different dimensions. Nonlinear Dyn 79(1):731–741MathSciNetCrossRefMATH
40.
Ding ZX, Shen Y (2016) Projective synchronization of nonidentical fractional-order neural networks based on sliding mode controller. Neural Netw 76:97–105CrossRef
41.
Liang S, Wu RC, Chen LP (2016) Adaptive pinning synchronization in fractional-order uncertain complex dynamical networks with delay. Phys A Stat Mech Appl 444:49–62MathSciNetCrossRefMATH
42.
43.
44.
Qin YX, Liu YQ, Wang L, Zheng ZX (1989) Stability of dynamic systems with delays. Science Press, Beijing
45.
Hu HY, Wang ZH (2002) Dynamics of controlled mechanical systems with delayed feedback. Springer, BerlinCrossRefMATH
46.
Tan MC, Pan Q, Zhou X (2016) Adaptive stabilization and synchronization of non-diffusively coupled complex networks with nonidentical nodes of different dimensions. Nonlinear Dyn 85(1):303–316MathSciNetCrossRefMATH
47.
Guo ZY, Huang LH (2009) LMI conditions for global robust stability of delayed neural networks with discontinuous neuron activations. Appl Math Comput 215(3):889–900MathSciNetMATH
48.
Zheng CD, Zhang XY, Wang ZS (2016) Mode and delay-dependent stochastic stability conditions of fuzzy neural networks with Markovian jump parameters. Neural Process Lett 43(1):195–217CrossRef
49.
Bhalekar S, Daftardar-Gejji V (2011) A predictor–corrector scheme for solving nonlinear delay differential equations of fractional order. Fract Calc Appl 1(5):1–9MATH
50.
Jia Q (2007) Hyperchaos generated from the Lorenz chaotic system and its control. Phys Lett A 366(3):217–222CrossRefMATH
51.
Li YX, Tang WKS, Chen GR (2005) Generating hyperchaos via state feedback control. Int J Bifurc Chaos 15(10):3367–3375CrossRef
52.
Belykh VN, Chua LO (1992) New type of strange attractor from a geometric model of Chua’s circuit. Int J Bifurc Chaos 2(3):697–704MathSciNetCrossRefMATH
53.
Wu ZY (2014) Cluster synchronization in colored community network with different order node dynamics. Commun Nonlinear Sci Numer Simul 19(4):1079–1087MathSciNetCrossRef
Metadata
Title
Global stability analysis of delayed complex-valued fractional-order coupled neural networks with nodes of different dimensions
Authors
Manchun Tan
Qi Pan
Publication date
18-12-2017
Publisher
Springer Berlin Heidelberg
Published in
International Journal of Machine Learning and Cybernetics / Issue 5/2019
Print ISSN: 1868-8071
Electronic ISSN: 1868-808X
DOI
https://doi.org/10.1007/s13042-017-0767-4

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