Top

Neural Computing and Applications

Published in:

24-08-2021 | Original Article

Exponential synchronization of fractional-order multilayer coupled neural networks with reaction-diffusion terms via intermittent control

Authors: Yao Xu, Fu Sun, Wenxue Li

Published in: Neural Computing and Applications | Issue 23/2021

Activate our intelligent search to find suitable subject content or patents.

search-config

AI-assisted search

Off

Abstract

In this paper, the issue of exponential synchronization of fractional-order multilayer coupled neural networks with reaction-diffusion terms is investigated by using periodically intermittent control. It deserves to mention that spatial diffusions, multilayer interactions and fractional dynamics are introduced to coupled neural networks at the same time. A novel fractional-order differential inequality is established on the basis of Caputo partial fractional operator. Moreover, to realize exponential synchronization of the underlying neural networks, some sufficient conditions are presented with the help of Lyapunov method and graph theory. Theoretical results show that the exponential convergence rate is dependent on the control gain and the order of fractional derivative. Finally, an illustrative numerical example is provided to further verify the feasibility and effectiveness of our results.

previous article A structure distinguishable graph attention network for knowledge base completion

next article Novel hybrid DNN approaches for speaker verification in emotional and stressful talking environments

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 340 Zeitschriften

aus folgenden Fachgebieten:

Bauwesen + Immobilien
Business IT + Informatik
Finance + Banking
Management + Führung
Marketing + Vertrieb
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 390 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Maschinenbau + Werkstoffe

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

über 102.000 Bücher
über 537 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Finance + Banking
Management + Führung
Marketing + Vertrieb
Maschinenbau + Werkstoffe
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Available only for authorised users

Newman MEJ (2003) The structure and function of complex networks. SLAM Rev 45(2):167–256MathSciNetMATH

Guo Y, Liu Y, Xu Y (2019) Synchronized stationary distribution of stochastic coupled systems based on graph theory. Math Meth Appl Sci 45:4444-4455

Wang ZX, He HB, Jiang GP, Cao JD (2021) Quasi-synchronization in heterogeneous harmonic oscillators with continuous and sampled coupling. IEEE Trans Syst Man Cybern -Syst 51(2):1267–1277

Zhou H, Song J, Li WX (2020) Razumikhin method to stability of delay coupled systems with hybrid switching diffusions. Nonlinear Anal Hybrid Syst 38:100934MathSciNet

Wang ZX, He HB, Jiang GP, Cao JD (2020) Distributed tracking in heterogeneous networks with asynchronous sampled-data control. IEEE Trans Ind Inform 16(12):7381–7391

Wu YB, Li YC, Li WX (2020) Almost surely exponential synchronization of complex dynamical networks under aperiodically intermittent discrete observations noise. IEEE T Cybern. https://doi.org/10.1109/TCYB.2020.3022296CrossRef

Wang ZX, He HB (2020) Asynchronous quasi-consensus of heterogeneous multiagent systems with nonuniform input delays. IEEE Trans Syst Man Cybern Syst 50(8):2815–2827

Chatterjee S, Sarkar S, Hore S, Dey N, Ashour AS, Balas VE (2017) Particle swarm optimization trained neural network for structural failure prediction of multistoried RC buildings. Neural Comput Appl 28(8):2005–2016

Xu DS, Liu Y, Liu M (2021) Finite-time synchronization of multi-coupling stochastic fuzzy neural networks with mixed delays via feedback control. Fuzzy Sets Syst 411:85–104MathSciNetMATH

10.

Wang YQ, Lu JQ, Li XD, Liang JL (2020) Synchronization of coupled neural networks under mixed impulsive effects: a novel delay inequality approach. Neural Netw 127:38–46MATH

11.

Xie X, Liu XZ, Xu HL (2019) Synchronization of delayed coupled switched neural networks: mode-dependent average impulsive interval. Neurocomputing 365:261–272

12.

Zhang ZQ, Ren L (2019) New sufficient conditions on global asymptotic synchronization of inertial delayed neural networks by using integrating inequality techniques. Nonlinear Dyn 95(2):905–917MathSciNetMATH

13.

Katchinskiy N, Goez HR, Dutta I, Godbout R, Elezzabi AY (2016) Novel method for neuronal nanosurgical connection. Sci Rep 6:20529

14.

Zhao X, Lu XJ, Zeng ZJ (2021) Synchronized stationary distribution for stochastic multi-links systems with Markov jump. Nonlinear Anal Hybrid Syst 40:101006MathSciNet

15.

Hou J, Huang YL, Ren SY (2019) Anti-synchronization analysis and pinning control of multi-weighted coupled neural networks with and without reaction-diffusion terms. Neurocomputing 330:78–93

16.

Tang HA, Wang JL, Wang LD, Hu XF, Zhou Y, Duan SK (2019) Impulsive control for passivity and exponential synchronization of coupled neural networks with multiple weights. J Frankl Inst Eng Appl Math 356(10):5434–5463MathSciNetMATH

17.

Zhang H, Zeng ZG, Han QL (2019) Synchronization of multiple reaction-diffusion neural networks with heterogeneous and unbounded time-varying delays. IEEE T Cybern 49(8):2980–2991

18.

Wang JL, Wu HN, Guo L (2011) Passivity and stability analysis of reaction-diffusion neural networks with dirichlet boundary conditions. IEEE Trans Neural Netw 22(12):2105–2116

19.

Ma Q, Feng G, Xu SY (2013) Delay-dependent stability criteria for reaction-diffusion neural networks with time-varying delays. IEEE T Cybern 43(6):1913–1920

20.

Lin JZ, Xu R, Li LC (2020) Turing-Hopf bifurcation of reaction-diffusion neural networks with leakage delay. Commun Nonlinear Sci Numer Simul 85:105241MathSciNetMATH

21.

Tyagi S, Abbas S, Kirane M (2018) Global asymptotic and exponential synchronization of ring neural network with reaction-diffusion term and unbounded delay. Neural Comput Appl 30(2):487–501

22.

Liu LJ, Chen WH, Lu XM (2018) Impulsive \(H_{\infty }\) synchronization for reaction-diffusion neural networks with mixed delays. Neurocomputing 272:481–494

23.

Yang XS, Song Q, Cao JD, Lu JQ (2019) Synchronization of coupled Markovian reaction-diffusion neural networks with proportional delays via quantized control. IEEE Trans Neural Netw Learn Syst 30(3):951–958MathSciNet

24.

Ezzat MA (2012) State space approach to thermoelectric fluid with fractional order heat transfer. Heat Mass Transf 48(1):71–82

25.

Lu C, Sun G, Zhang Y (2021) Stationary distribution and extinction of a multi-stage HIV model with nonlinear stochastic perturbation. J Appl Math Comput. https://doi.org/10.1007/s12190-021-01530-z

26.

Niedziela M, Wlazlo J (2008) Notes on computational aspects of the fractional-order viscoelastic model. J Eng Math 108(1):91–105MathSciNetMATH

27.

Li HL, Hu C, Cao JD, Jiang HJ, Alsaedi A (2019) Quasi-projective and complete synchronization of fractional-order complex-valued neural networks with time delays. Neural Netw 118:102–109MATH

28.

Xu Y, Yu JT, Li WX, Feng JQ (2021) Global asymptotic stability of fractional-order competitive neural networks with multiple time-varying-delay links. Appl Math Comput 389:125498MathSciNetMATH

29.

Peng X, Wu HQ (2020) Non-fragile robust finite-time stabilization and H infinity performance analysis for fractional-order delayed neural networks with discontinuous activations under the asynchronous switching. Neural Comput Appl 32(8):4045–4071

30.

Xu Y, Gao S, Li WX (2020) Exponential stability of fractional-order complex multi-links networks with aperiodically intermittent control. IEEE Trans Neural Netw Learn Syst. https://doi.org/10.1109/TNNLS.2020.3016672CrossRef

31.

Xu Y, Wang Q, Li WX, Feng JQ (2021) Stability and synchronization of fractional-order delayed multilink complex networks with nonlinear hybrid couplings. Math Meth Appl Sci 44(5):3356–3375MathSciNetMATH

32.

Stamova I, Stamov G (2017) Mittag-Leffler synchronization of fractional neural networks with time-varying delays and reaction-diffusion terms using impulsive and linear controllers. Neural Netw 96:22–32MATH

33.

Lv YJ, Hu C, Yu J, Jiang HJ, Huang TW (2020) Edge-based fractional-order adaptive strategies for synchronization of fractional-order coupled networks with reaction-diffusion terms. IEEE T Cybern 50(4):1582–1594

34.

Sun WJ, Ren GJ, Yu YG, Hai XD (2020) Global synchronization of reaction-diffusion fractional-order memristive neural networks with time delay and unknown parameters. Complexity 2020:4145826MATH

35.

Stamova IM, Simeonov S (2018) Delayed reaction-diffusion cellular neural networks of fractional order: Mittag-Leffler stability and synchronization. J Comput Nonlinear Dyn 13(1):11–15

36.

Xu Y, Chu CY, Li WX (2018) Quantized feedback control scheme on coupled systems with time delay and distributed delay: a finite-time inner synchronization analysis. Appl Math Comput 337:315–328MathSciNetMATH

37.

Liu Y, Wang M, Chu DH, Su H (2021) Feedback control based on discrete-time state observations on synchronization of stochastic impulsive coupled systems. Nonlinear Anal Hybrid Syst 39:100987MathSciNet

38.

Li S, Zhang BG, Li WX (2021) Stabilisation of multi-weights stochastic complex networks with time-varying delay driven by G-Brownian motion via aperiodically intermittent adaptive control. Int J Control 94(1):7–20MathSciNetMATH

39.

Zhou PP, Cai SM, Shen JW, Liu ZR (2018) Adaptive exponential cluster synchronization in colored community networks via aperiodically intermittent pinning control. Nonlinear Dyn 92(3):905–921MATH

40.

Liu Y, Liu J, Li WX (2020) Stabilization of highly nonlinear stochastic coupled systems via periodically intermittent control. Control IEEE Trans Autom. https://doi.org/10.1109/TAC.2020.3036035CrossRef

41.

Xu LG, Liu W, Hu HX, Zhou WS (2019) Exponential ultimate boundedness of fractional-order differential systems via periodically intermittent control. Nonlinear Dyn 96(2):1665–1675MATH

42.

Xu Y, Li Q, Li WX (2019) Periodically intermittent discrete observation control for synchronization of fractional-order coupled systems. Commun Nonlinear Sci Numer Simul 74:219–235MathSciNetMATH

43.

Podlubny I (1999) Fractional differential equations. Academic Press, New YorkMATH

44.

Hu C, Jiang HJ, Teng ZD (2010) Impulsive control and synchronization for delayed neural networks with reaction-diffusion terms. IEEE Trans Neural Netw 21(1):67–81

45.

Li MY, Shuai ZS (2010) Global-stability problem for coupled systems of differential equations on networks. J Differ Equ 248(1):1–20MathSciNetMATH

46.

Jia Q, Tang WKS (2020) Event-based tracking consensus for multiagent systems with volatile control gain. IEEE T Cybern. https://doi.org/10.1109/TCYB.2020.3027039CrossRef

47.

Jia Q, Mwanandiye ES, Tang WKS (2020) Master-slave synchronization of delayed neural networks with time-varying control. IEEE Trans Neural Netw Learn Syst. https://doi.org/10.1109/TNNLS.2020.2996224CrossRef

48.

Cai SM, Lei XQ, Liu ZR (2016) Outer synchronization between two hybrid-coupled delayed dynamical networks via aperiodically adaptive intermittent pinning control. Complexity 21(S2):593–605MathSciNet

49.

Zhou PP, Shi JY, Cai SM (2020) Pinning synchronization of directed networks with delayed complex-valued dynamical nodes and mixed coupling via intermittent control. J Frankl Inst Eng Appl Math 357(17):12840–12869MathSciNetMATH

50.

Wang PF, Wang RF, Su H (2021) Stability of time-varying hybrid stochastic delayed systems with application to aperiodically intermittent stabilization. IEEE T Cybern. https://doi.org/10.1109/TCYB.2021.3052042CrossRef

Title: Exponential synchronization of fractional-order multilayer coupled neural networks with reaction-diffusion terms via intermittent control
Authors: Yao Xu
Fu Sun
Wenxue Li
Publication date: 24-08-2021
Publisher: Springer London
Published in: Neural Computing and Applications / Issue 23/2021
Print ISSN: 0941-0643
Electronic ISSN: 1433-3058
DOI: https://doi.org/10.1007/s00521-021-06214-0

Springer Professional

Abstract

Please log in to get access to your license.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft"

Springer Professional "Technik"

Springer Professional "Wirtschaft+Technik"

Other articles of this Issue 23/2021

Hybrid intelligent framework for one-day ahead wind speed forecasting

Optimisation of used nuclear fuel canister loading using a neural network and genetic algorithm

Spatial bound whale optimization algorithm: an efficient high-dimensional feature selection approach

On the modeling of the annual corrosion rate in main cables of suspension bridges using combined soft computing model and a novel nature-inspired algorithm

An improved PTS scheme based on a novel discrete invasive weed optimization algorithm for PAPR reduction in the UFMC signal

Classification of organic and conventional olives using convolutional neural networks

Premium Partner