Top

Cognitive Neurodynamics

Published in:

28-06-2019 | Research Article

Synchronization control of quaternion-valued memristive neural networks with and without event-triggered scheme

Authors: Ruoyu Wei, Jinde Cao

Published in: Cognitive Neurodynamics | Issue 5/2019

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

search-config

AI-assisted search

Off

Abstract

In this paper, the real-valued memristive neural networks (MNNs) are extended to quaternion field, a new class of neural networks named quaternion-valued memristive neural networks (QVMNNs) is then established. The problem of master-slave synchronization of this type of networks is investigated in this paper. Two types of controllers are designed: the traditional feedback controller and the event-triggered controller. Corresponding synchronization criteria are then derived based on Lyapunov method. Moreover, it is demonstrated that Zeno behavior can be avoided in case of the event-triggered strategy proposed in this work. Finally, corresponding simulation examples are proposed to demonstrate the correctness of the proposed results derived in this work.

previous article Adaptive sparse coding based on memristive neural network with applications

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

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"

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

Adler SL (1995) Quaternionic quantum mechanics and quantum fields. Oxford University Press, New York

Bao H, Cao J (2014) Projective synchronization of fractional order memristor-based neural networks. Neural Netw 63:1–9CrossRefPubMed

Bao H, Park JH, Cao J (2016) Exponential synchronization of coupled stochastic memristor-based neural networks with time-varying probabilistic delay coupling and impulsive delay. IEEE Trans Neural Netw Learn Syst 27(1):190–201CrossRefPubMed

Cao Y (2019) Bifurcations in an Internet congestion control system with distributed delay. Appl Math Comput 347:54–63

Cao J, Guerrini L, Cheng Z (2019) Stability and Hopf bifurcation of controlled complex networks model with two delays. Appl Math Comput 343:21–29

Chen J, Zeng Z, Jiang P (2014) Global Mittag-Leffler stability and synchronization of memristor-based fractional-order neural networks. Neural Netw 51:1–8CrossRefPubMed

Chen L, Wu R, Cao J, Liu J (2015) Stability and synchronization of memristor-based fractional-order delayed neural networks. Neural Netw 71:37–44CrossRefPubMed

Chen X, Li Z, Song Q, Hu J, Tan Y (2017) Robust stability analysis of quaternion-valued neural networks with time delays and parameter uncertainties. Neural Netw 91:55–65CrossRefPubMed

Chen X, Song Q, Li Z, Zhao Z, Liu Y (2018) Stability analysis of continuous-time and discrete-time quaternion-valued neural networks with linear threshold neurons. IEEE Trans Neural Netw Learn Syst 29(7):2769–2781PubMed

Chen X, Song Q (2017) State estimation for quaternion-valued neural networks with multiple time delays. IEEE Trans Syst Man Cybern Syst. https://doi.org/10.1109/TSMC.2017.2776940

Chua LO (1971) Memristor-the missing circuit element. IEEE Trans Circuit Theory 18:507–519CrossRef

Dharani S, Rakkiyappan R, Cao J, Alsaedi A (2017) Synchronization of generalized reaction-diffusion neural networks with time-varying delays based on general integral inequalities and sampled-data control approach. Cogn Neurodyn 11(4):369–381CrossRefPubMedPubMedCentral

Ding X, Cao J, Alsaedi A, Hayat T (2017) Robust fixed-time synchronization for uncertain complex-valued neural networks with discontinuous activation functions. Neural Netw 90:42–55CrossRefPubMed

Guo Z, Gong S, Wen S, Huang T (2018) Event-based synchronization control for memristive neural networks with time-varying delay. IEEE Trans Cybern. https://doi.org/10.1109/TCYB.2018.2839686

Halanay A (1966) Differential equations: stability, oscillations, time lags, vol 23. Academic, New York

Huang C, Liu B (2019) New studies on dynamic analysis of inertial neural networks involving non-reduced order method. Neurocomputing 325:283–287CrossRef

Huang C, Zhang H (2019) Periodicity of non-autonomous inertial neural networks involving proportional delays and non-reduced order method. Int J Biomath 12(2):1950016CrossRef

Huang C, Yang Z, Yi T, Zou X (2014) On the basins of attraction for a class of delay differential equations with non-monotone bistable nonlinearities. J Differ Equ 256:2101–2114CrossRef

Huang C, Su R, Cao J, Xiao S (2019) Asymptotically stable of high-order neutral cellular neural networks with proportional delays and D operators. Math Comput Simul. https://doi.org/10.1016/j.matcom.2019.06.001 CrossRef

Isokawa T, Kusakabe T, Matsui N, Peper F (2003) Quaternion neural network and its application. In: Proc. 7th int. conf. KES, Oxford, U.K., pp 318–324

Li L, Ho D, Cao J, Lu J (2016) Pinning cluster synchronization in an array of coupled neural networks under event-based mechanism. Neural Netw 76:1–12CrossRefPubMed

Liu Y, Zhang D, Lu J, Cao J (2016) Global \(\mu \)-stability criteria for quaternion-valued neural networks with unbounded time-varying delays. Inf Sci 360:273–288CrossRef

Liu H, Wang Z, Shen B, Liu X (2017a) Event-triggered state estimation for delayed stochastic memristive neural networks with missing measurements: the discrete time case. IEEE Trans Neural Netw Learn Syst 29(8):3726–3737PubMed

Liu Y, Zhang D, Lu J (2017b) Global exponential stability for quaternionvalued recurrent neural networks with time-varying delays. Nonlinear Dyn 87(1):553–565CrossRef

Liu Y, Zhang D, Lou J, Lu J, Cao J (2018) Stability analysis of quaternion-valued neural networks: decomposition and direct approaches. IEEE Trans Neural Netw Learn Syst 29(9):4201–4211CrossRefPubMed

Liu D, Zhu S, Sun K Global anti-synchronization of complex-valued memristive neural networks with time delays. IEEE Trans Cybern. https://doi.org/10.1109/TCYB.2018.2812708

Nakamura O, Tateno K (2019) Random pulse induced synchronization and resonance in uncoupled non-identical neuron models. Cogn Neurodyn 13(3):303–312CrossRefPubMed

Qin S, Feng J, Song J, Wen X, Xu C (2018) A one-layer recurrent neural network for constrained complex-variable convex optimization. IEEE Trans Neural Netw Learn Syst 29(3):534–544CrossRefPubMed

Ravishankar A (2018) An oscillatory neural network model that demonstrates the benefits of multisensory learning. Cogn Neurodyn 12(5):481–499CrossRef

Sahoo A, Xu H, Jagannathan S (2016) Neural network-based event-triggered state feedback control of nonlinear continuous-time systems. IEEE Trans Neural Netw Learn Syst 27(3):497–509CrossRefPubMed

Simmons GF (1992) Calculus gems: brief lives and memorable mathematics. McGraw-Hill, New York

Song Q, Chen X (2018) Multistability analysis of quaternion-valued neural networks with time delays. IEEE Trans Neural Netw Learn Syst 29(11):5430–5440CrossRefPubMed

Strukov D, Snider G, Stewart D, Williams RS (2008) The missing memristor found. Nature 453:80–83CrossRefPubMed

Took CC, Mandic DP (2009) The quaternion LMS algorithm for adaptive filtering of hypercomplex processes. IEEE Trans Signal Process 57(4):1316–1327CrossRef

Tu Z, Cao J, Alsaedi A, Hayat T (2017) Global dissipativity analysis for delayed quaternion-valued neural networks. Neural Netw 89:97–104CrossRefPubMed

Wang L, Wang Z, Wei G, Alsaadi F (2018) Finite-time state estimation for recurrent delayed neural networks with component-based event-triggering protocol. IEEE Trans Neural Netw Learn Syst 29(4):1046–1057CrossRefPubMed

Wei R, Cao J, Alsaedi A (2018) Finite-time and fixed-time synchronization analysis of inertial memristive neural networks with time-varying delays. Cogn Neurodyn 12(1):121–134CrossRefPubMed

Wen L, Yu Y, Wang W (2008) Generalized Halanay inequalities for dissipativity of Volterra functional differential equations. J Math Anal Appl 347(1):169–178CrossRef

Wu A, Zeng Z (2014) Lagrange stability of memristive neural networks with discrete and distributed delays. IEEE Trans Neural Netw Learn Syst 25(4):690–703CrossRefPubMed

Xia Y, Jahanchahi C, Mandic DP (2015) Quaternion-valued echo state networks. IEEE Trans Neural Netw Learn Syst 26(4):663–673CrossRefPubMed

Yang C, Huang L, Li F (2018) Exponential synchronization control of discontinuous nonautonomous networks and autonomous coupled networks. Complexity 2018:1–10

Zhang G, Shen Y (2014) Exponential synchronization of delayed memristor-based chaotic neural networks via periodically intermittent control. Neural Netw 55:1–10CrossRefPubMed

Zou C, Kou K, Wang Y (2016) Quaternion collaborative and sparse representation with application to color face recognition. IEEE Trans Image Process 25(7):3287–3302CrossRef

Title: Synchronization control of quaternion-valued memristive neural networks with and without event-triggered scheme
Authors: Ruoyu Wei
Jinde Cao
Publication date: 28-06-2019
Publisher: Springer Netherlands
Published in: Cognitive Neurodynamics / Issue 5/2019
Print ISSN: 1871-4080
Electronic ISSN: 1871-4099
DOI: https://doi.org/10.1007/s11571-019-09545-w

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+Technik"

Springer Professional "Technik"

Springer Professional "Wirtschaft"

Other articles of this Issue 5/2019

The frequent subgraphs of the connectome of the human brain

The individuality index: a measure to quantify the degree of inter-individual, spatial variability in intra-cerebral brain electric and metabolic activity

Scale-free behaviour and metastable brain-state switching driven by human cognition, an empirical approach

Adaptive sparse coding based on memristive neural network with applications

Prediction of epilepsy seizure from multi-channel electroencephalogram by effective connectivity analysis using Granger causality and directed transfer function methods

Points and lines inside human brains