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Published in: Cognitive Neurodynamics 1/2018

21-09-2017 | Research Article

Finite-time and fixed-time synchronization analysis of inertial memristive neural networks with time-varying delays

Authors: Ruoyu Wei, Jinde Cao, Ahmed Alsaedi

Published in: Cognitive Neurodynamics | Issue 1/2018

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Abstract

This paper investigates the finite-time synchronization and fixed-time synchronization problems of inertial memristive neural networks with time-varying delays. By utilizing the Filippov discontinuous theory and Lyapunov stability theory, several sufficient conditions are derived to ensure finite-time synchronization of inertial memristive neural networks. Then, for the purpose of making the setting time independent of initial condition, we consider the fixed-time synchronization. A novel criterion guaranteeing the fixed-time synchronization of inertial memristive neural networks is derived. Finally, three examples are provided to demonstrate the effectiveness of our main results.

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Literature
go back to reference Abdurahman A, Jiang H, Teng Z (2015) Finite-time synchronizing for memrisor-based neural networks with time-varying delays. Neural Netw 69:20–28CrossRefPubMed Abdurahman A, Jiang H, Teng Z (2015) Finite-time synchronizing for memrisor-based neural networks with time-varying delays. Neural Netw 69:20–28CrossRefPubMed
go back to reference Balasubramaniam P, Chandran R, Jeeva S (2011) Synchronization of chaotic nonlinear continuous neural networks with time-varying delay. Cogn Neurodyn 5:361–371CrossRefPubMedPubMedCentral Balasubramaniam P, Chandran R, Jeeva S (2011) Synchronization of chaotic nonlinear continuous neural networks with time-varying delay. Cogn Neurodyn 5:361–371CrossRefPubMedPubMedCentral
go back to reference Bao H, Cao J (2016) Finite-time generalized synchronization of nonidentical delayed chaotic systems. Nonlinear Anal: Model Control 21(3):306–324 Bao H, Cao J (2016) Finite-time generalized synchronization of nonidentical delayed chaotic systems. Nonlinear Anal: Model Control 21(3):306–324
go back to reference Bhat S, Bernstein D (2000) Finite-time stability of continuous autonomous systems. SIAM J Control Optim 38(3):751–766CrossRef Bhat S, Bernstein D (2000) Finite-time stability of continuous autonomous systems. SIAM J Control Optim 38(3):751–766CrossRef
go back to reference Cao J, Lu J (2006) Adaptive synchronization of neural networks with or without time-varying delays. Chaos 16(1):013133CrossRefPubMed Cao J, Lu J (2006) Adaptive synchronization of neural networks with or without time-varying delays. Chaos 16(1):013133CrossRefPubMed
go back to reference Cao J, Wan Y (2014) Matrix measure strategies for stability and synchronization of inertial neural network with time-delays. Neural Netw 53:165–172CrossRefPubMed Cao J, Wan Y (2014) Matrix measure strategies for stability and synchronization of inertial neural network with time-delays. Neural Netw 53:165–172CrossRefPubMed
go back to reference 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 L, Wu R, Cao J, Liu J (2015) Stability and synchronization of memristor-based fractional-order delayed neural networks. Neural Netw 71:37–44CrossRefPubMed
go back to reference Chua LO (1971) Memristor-the missing circuit element. IEEE Trans Circuit Theory 18:507–519CrossRef Chua LO (1971) Memristor-the missing circuit element. IEEE Trans Circuit Theory 18:507–519CrossRef
go back to reference Dong T, Liao X, Huang T (2012) Hopf-pitchfork bifurcation in an inertial two-neuron system with time delay. Neurocomputing 97:223–232CrossRef Dong T, Liao X, Huang T (2012) Hopf-pitchfork bifurcation in an inertial two-neuron system with time delay. Neurocomputing 97:223–232CrossRef
go back to reference Filippov AF, Arscott FM (2013) Differential equations with discontinuous right hand sides: control systems. Springer, Berlin Filippov AF, Arscott FM (2013) Differential equations with discontinuous right hand sides: control systems. Springer, Berlin
go back to reference He X, Li C, Shu Y (2012) Bogdanov–Takens bifurcation in a single inertial neural model with delay. Neurocomputing 89:193–201CrossRef He X, Li C, Shu Y (2012) Bogdanov–Takens bifurcation in a single inertial neural model with delay. Neurocomputing 89:193–201CrossRef
go back to reference Hu J, Cao J, Alofi A, Abdullah A, Elaiw A (2015) Pinning synchronization of coupled inertial delayed neural networks. Cogn Neurodyn 9:341–350CrossRefPubMed Hu J, Cao J, Alofi A, Abdullah A, Elaiw A (2015) Pinning synchronization of coupled inertial delayed neural networks. Cogn Neurodyn 9:341–350CrossRefPubMed
go back to reference Ke Y, Miao C (2013) Stability analysis of inertial Cohen–Grossberg-type neural networks with time delays. Neurocomputing 117:196–205CrossRef Ke Y, Miao C (2013) Stability analysis of inertial Cohen–Grossberg-type neural networks with time delays. Neurocomputing 117:196–205CrossRef
go back to reference Ke Y, Miao C (2013) Stability and existence of periodic solutions in inertial BAM neural networks with time delay. Neural Comput Appl 23(3):1089–1099 Ke Y, Miao C (2013) Stability and existence of periodic solutions in inertial BAM neural networks with time delay. Neural Comput Appl 23(3):1089–1099
go back to reference Li N, Cao J (2016) Lag synchronization of memristor-based coupled neural networks via \(\omega \)-measure. IEEE Trans Neural Netw Learn Syst 27(3):169–182CrossRef Li N, Cao J (2016) Lag synchronization of memristor-based coupled neural networks via \(\omega \)-measure. IEEE Trans Neural Netw Learn Syst 27(3):169–182CrossRef
go back to reference Li C, Chen G, Yu J (2004) Hopf bifurcation and chaos in a single inertial neuron model with time delay. Eur Phys J B 41:337–343CrossRef Li C, Chen G, Yu J (2004) Hopf bifurcation and chaos in a single inertial neuron model with time delay. Eur Phys J B 41:337–343CrossRef
go back to reference Liu Q, Liao X, Guo S, Wu Y (2009) Stability of bifurcating periodic solution for a single delayed inertial neuron model under periodic excitation. Nonlinear Anal: Real World Appl 10:2384–2395CrossRef Liu Q, Liao X, Guo S, Wu Y (2009) Stability of bifurcating periodic solution for a single delayed inertial neuron model under periodic excitation. Nonlinear Anal: Real World Appl 10:2384–2395CrossRef
go back to reference Liu Q, Liao X, Liu Y (2009) Dynamics of an inertial two-neuron system with time delay. Nonlinear Dyn 58(3):573–609CrossRef Liu Q, Liao X, Liu Y (2009) Dynamics of an inertial two-neuron system with time delay. Nonlinear Dyn 58(3):573–609CrossRef
go back to reference Liu X, Ho DWC, Yu W, Cao J (2014) A new switching design to finite-time stabilization of nonlinear systems with applications to neural networks. Neural Netw 57:94–102CrossRefPubMed Liu X, Ho DWC, Yu W, Cao J (2014) A new switching design to finite-time stabilization of nonlinear systems with applications to neural networks. Neural Netw 57:94–102CrossRefPubMed
go back to reference Liu X, Su H, Chen M (2016) A switching approach to designing finite-time synchronization controllers of coupled neural networks. IEEE Trans Neural Netw Learn Syst 27(2):471–482CrossRefPubMed Liu X, Su H, Chen M (2016) A switching approach to designing finite-time synchronization controllers of coupled neural networks. IEEE Trans Neural Netw Learn Syst 27(2):471–482CrossRefPubMed
go back to reference Polyakov A (2012) Nonlinear feedback design for fixed-time stabilization of linear control systems. IEEE Trans Autom Control 57(8):2106–2110CrossRef Polyakov A (2012) Nonlinear feedback design for fixed-time stabilization of linear control systems. IEEE Trans Autom Control 57(8):2106–2110CrossRef
go back to reference Rakkiyappan R, Velmurugan G, Cao J (2015) Stability analysis of memristor-based fractional-order neural networks with different memductance functions. Cogn Neurodyn 9:145–177CrossRefPubMed Rakkiyappan R, Velmurugan G, Cao J (2015) Stability analysis of memristor-based fractional-order neural networks with different memductance functions. Cogn Neurodyn 9:145–177CrossRefPubMed
go back to reference Rakkiyappan R, Premalatha S, Chandrasekar A, Cao J (2016) Stability and synchronization of innertial memristive neural networks with time delays. Cogn Neurodyn 10:437–451CrossRefPubMedPubMedCentral Rakkiyappan R, Premalatha S, Chandrasekar A, Cao J (2016) Stability and synchronization of innertial memristive neural networks with time delays. Cogn Neurodyn 10:437–451CrossRefPubMedPubMedCentral
go back to reference Shen J, Cao J (2011) Finite-time synchronization of coupled neural networks via discontinuous controllers. Cogn Neurodyn 5(4):372–385CrossRef Shen J, Cao J (2011) Finite-time synchronization of coupled neural networks via discontinuous controllers. Cogn Neurodyn 5(4):372–385CrossRef
go back to reference Wan Y, Cao J, Wen G, Yu W (2016) Robust fixed-time synchronization of delayed Cohen–Grossburg neural networks. Neural Netw 73:86–94CrossRefPubMed Wan Y, Cao J, Wen G, Yu W (2016) Robust fixed-time synchronization of delayed Cohen–Grossburg neural networks. Neural Netw 73:86–94CrossRefPubMed
go back to reference Wang W, Li L, Peng H, Xiao J, Yang Y (2014) Synchronization control of memristor-based recurrent neural networks with perturbations. Neural Netw 53:8–14CrossRefPubMed Wang W, Li L, Peng H, Xiao J, Yang Y (2014) Synchronization control of memristor-based recurrent neural networks with perturbations. Neural Netw 53:8–14CrossRefPubMed
go back to reference Wen S, Bao G, Zeng Z, Chen Y, Huang T (2013) Global exponential synchronization of memristor-based recurrent neural networks with time-varying delays. Neural Netw 48:195–203CrossRefPubMed Wen S, Bao G, Zeng Z, Chen Y, Huang T (2013) Global exponential synchronization of memristor-based recurrent neural networks with time-varying delays. Neural Netw 48:195–203CrossRefPubMed
go back to reference Wheeler WD, Schieve WC (1997) Stability and chaos in an inertial two-neuron system. Phys B 105:267–284 Wheeler WD, Schieve WC (1997) Stability and chaos in an inertial two-neuron system. Phys B 105:267–284
go back to reference Wu A, Zeng Z (2015) Global Mittag–Leffler stabilization of fractional-order memristive neural networks. IEEE Trans Neural Netw Learn Syst 3:1–12 Wu A, Zeng Z (2015) Global Mittag–Leffler stabilization of fractional-order memristive neural networks. IEEE Trans Neural Netw Learn Syst 3:1–12
go back to reference Xu L, Wang X (1983) Mathematical analysis method and examples. Higher Education Press, Beijing Xu L, Wang X (1983) Mathematical analysis method and examples. Higher Education Press, Beijing
go back to reference Yang X, Cao J, Ho DWC (2015) Exponential synchronization of discontinuous neural networks with time-varying mixed delay via state feedback and impulsive control. Cogn Neurodyn 9:113–128CrossRefPubMed Yang X, Cao J, Ho DWC (2015) Exponential synchronization of discontinuous neural networks with time-varying mixed delay via state feedback and impulsive control. Cogn Neurodyn 9:113–128CrossRefPubMed
go back to reference Yang X, Cao J, Liang J Exponential Synchronization of memeristive neural networks with delays:Interval matrix method. IEEE Trans Neural Netw Learn Syst 28(8):1878–1888CrossRef Yang X, Cao J, Liang J Exponential Synchronization of memeristive neural networks with delays:Interval matrix method. IEEE Trans Neural Netw Learn Syst 28(8):1878–1888CrossRef
go back to reference Zhang Z, Quan Z (2015) Global exponential stability via inequality technique for inertial BAM neural networks with time delays. Neurocomputing 151(3):1316–1326CrossRef Zhang Z, Quan Z (2015) Global exponential stability via inequality technique for inertial BAM neural networks with time delays. Neurocomputing 151(3):1316–1326CrossRef
go back to reference Zhang W, Li C, Huang T, Tan J (2015) Exponential stability of inertial BAM neural networks with time-varying delay via periodically intermittent control. Neural Comput Appl 26:1781–1787CrossRef Zhang W, Li C, Huang T, Tan J (2015) Exponential stability of inertial BAM neural networks with time-varying delay via periodically intermittent control. Neural Comput Appl 26:1781–1787CrossRef
Metadata
Title
Finite-time and fixed-time synchronization analysis of inertial memristive neural networks with time-varying delays
Authors
Ruoyu Wei
Jinde Cao
Ahmed Alsaedi
Publication date
21-09-2017
Publisher
Springer Netherlands
Published in
Cognitive Neurodynamics / Issue 1/2018
Print ISSN: 1871-4080
Electronic ISSN: 1871-4099
DOI
https://doi.org/10.1007/s11571-017-9455-z

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