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Published in: International Journal of Machine Learning and Cybernetics 1/2016

01-02-2016 | Original Article

Synchronization of delayed Markovian jump memristive neural networks with reaction–diffusion terms via sampled data control

Authors: Ruoxia Li, Hongzhi Wei

Published in: International Journal of Machine Learning and Cybernetics | Issue 1/2016

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Abstract

This paper is concerned with the sampled-data synchronization issues for delayed memristive neural networks with Markovian jumping and reaction–diffusion terms. In the frame work of inequality techniques and a useful Lyapunov functional, some new testable algebraic criteria are obtained to ensure the stability of the error system, and thus, the master system can synchronize with the slave system. Finally, an illustrative example is exploited to demonstrate the performance and effectiveness of the developed approach.

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Literature
1.
go back to reference Chua L (1971) Memristor—the missing circuit element. IEEE Trans Circuit Theory 18:507–519CrossRef Chua L (1971) Memristor—the missing circuit element. IEEE Trans Circuit Theory 18:507–519CrossRef
2.
go back to reference Strukov D, Snider G, Stewart D, Williams R (2008) The missing memristor found. Nature 453:80–83CrossRef Strukov D, Snider G, Stewart D, Williams R (2008) The missing memristor found. Nature 453:80–83CrossRef
3.
go back to reference Corinto F, Ascoli A, Gilli M (2011) Nonlinear dynamics of memristor oscillators. IEEE Trans Circuits Syst I 58:1323–1336MathSciNetCrossRef Corinto F, Ascoli A, Gilli M (2011) Nonlinear dynamics of memristor oscillators. IEEE Trans Circuits Syst I 58:1323–1336MathSciNetCrossRef
4.
5.
go back to reference Messias M, Nespoli C, Botta V (2010) Hopf bifurcation from lines of equilibria without parameters in memristor oscillators. Int J Bifurcation Chaos 20:437–450MATHMathSciNetCrossRef Messias M, Nespoli C, Botta V (2010) Hopf bifurcation from lines of equilibria without parameters in memristor oscillators. Int J Bifurcation Chaos 20:437–450MATHMathSciNetCrossRef
7.
go back to reference Petras I (2010) Fractional-order memristor-based Chua’s circuit. IEEE Trans Circuits Syst II Exp Briefs 57:975–979CrossRef Petras I (2010) Fractional-order memristor-based Chua’s circuit. IEEE Trans Circuits Syst II Exp Briefs 57:975–979CrossRef
8.
go back to reference Tsang E, Wang X, Yeung D (2000) Improving learning accuracy of fuzzy decision trees by hybrid neural networks. IEEE Trans Fuzzy Syst 8:601–614CrossRef Tsang E, Wang X, Yeung D (2000) Improving learning accuracy of fuzzy decision trees by hybrid neural networks. IEEE Trans Fuzzy Syst 8:601–614CrossRef
9.
go back to reference Wang X, Dong C, Fan T (2007) Training T-S norm neural networks to refine weights for fuzzy if-then rules. Neurocomputing 70:2581–2587CrossRef Wang X, Dong C, Fan T (2007) Training T-S norm neural networks to refine weights for fuzzy if-then rules. Neurocomputing 70:2581–2587CrossRef
10.
go back to reference Roska T, Chua L (1992) Cellular neural networks with nonlinear and delay-type tempiate. Int J Circuit Theory Appl 20:469–481MATHCrossRef Roska T, Chua L (1992) Cellular neural networks with nonlinear and delay-type tempiate. Int J Circuit Theory Appl 20:469–481MATHCrossRef
11.
go back to reference Li H, Chen B, Zhou Q, Qian W (2009) Robust stability for uncertain delayed fuzzy Hopfield neural networks with Markovian jumping parameters. IEEE Trans Syst Man Cybern B Cybern 39:94–102CrossRef Li H, Chen B, Zhou Q, Qian W (2009) Robust stability for uncertain delayed fuzzy Hopfield neural networks with Markovian jumping parameters. IEEE Trans Syst Man Cybern B Cybern 39:94–102CrossRef
12.
go back to reference Wang Z, Liu Y, Yu L, Liu X (2006) Exponential stability of delayed recurrent neural networks with Markovian jumping parameters. Phys Lett A 356:346–352MATHCrossRef Wang Z, Liu Y, Yu L, Liu X (2006) Exponential stability of delayed recurrent neural networks with Markovian jumping parameters. Phys Lett A 356:346–352MATHCrossRef
13.
go back to reference Wu Z, Shi P, Su H, Chu J (2011) Passivity analysis for discrete-time stochastic Markovian jump neural networks with mixed time delays. IEEE Trans Neural Netw 22:1566–1575CrossRef Wu Z, Shi P, Su H, Chu J (2011) Passivity analysis for discrete-time stochastic Markovian jump neural networks with mixed time delays. IEEE Trans Neural Netw 22:1566–1575CrossRef
14.
go back to reference Zhang H, Wang Y (2008) Stability analisis of Markovian jumping stochastic Cohen–Grossberg neural networks with mixed time delays. IEEE Trans Neural Netw 19:366–370CrossRef Zhang H, Wang Y (2008) Stability analisis of Markovian jumping stochastic Cohen–Grossberg neural networks with mixed time delays. IEEE Trans Neural Netw 19:366–370CrossRef
15.
go back to reference Zhu Q, Cao J (2011) Exponential stability of neural networks with both Markovian jump parameters and mixed time delays. IEEE Trans Syst Man Cybern B Cybern 41:341–353 Zhu Q, Cao J (2011) Exponential stability of neural networks with both Markovian jump parameters and mixed time delays. IEEE Trans Syst Man Cybern B Cybern 41:341–353
16.
go back to reference Landsman A, Schwartz I (2007) Complete chaotic synchronization in mutually coupled time-delay systems. Phys Rev E 5:26–33 Landsman A, Schwartz I (2007) Complete chaotic synchronization in mutually coupled time-delay systems. Phys Rev E 5:26–33
17.
go back to reference Huang T, Li C, Liao X (2007) Synchronization of a class of coupled chaotic delays systems with parameter mismatch. Chaos 17:33–121 Huang T, Li C, Liao X (2007) Synchronization of a class of coupled chaotic delays systems with parameter mismatch. Chaos 17:33–121
18.
go back to reference Cui B, Lou X (2009) Synchronization of chaotic recurrent neural networks with time-varying delays using nonlinear feedback control. Chaos Solitons Fract 39:288–294MATHMathSciNetCrossRef Cui B, Lou X (2009) Synchronization of chaotic recurrent neural networks with time-varying delays using nonlinear feedback control. Chaos Solitons Fract 39:288–294MATHMathSciNetCrossRef
19.
go back to reference Gan Q, Xu R, Kang X (2011) Synchronization of chaotic neural networks with mixed time delays. Commun Nonlinear Sci Numer Simul 16:966–974MATHMathSciNetCrossRef Gan Q, Xu R, Kang X (2011) Synchronization of chaotic neural networks with mixed time delays. Commun Nonlinear Sci Numer Simul 16:966–974MATHMathSciNetCrossRef
20.
go back to reference Zhan M, Wei G, Lai C (2002) Transition from intermittency to periodicity in lag synchronization in coupled Rössler oscillators. Phys Rev E 65:36–40CrossRef Zhan M, Wei G, Lai C (2002) Transition from intermittency to periodicity in lag synchronization in coupled Rössler oscillators. Phys Rev E 65:36–40CrossRef
21.
go back to reference Xu D, Chee C (2002) Controlling the ultimate state of projective synchronization in chaotic systems of arbitrary dimension. Phys Rev E 66:46–50CrossRef Xu D, Chee C (2002) Controlling the ultimate state of projective synchronization in chaotic systems of arbitrary dimension. Phys Rev E 66:46–50CrossRef
22.
go back to reference Li X, Bohner M (2010) Exponential synchronization of chaotic neural networks with mixed delays and impulsive effects via output coupling with delay feedback. Math Comput Model 52:643–653MATHMathSciNetCrossRef Li X, Bohner M (2010) Exponential synchronization of chaotic neural networks with mixed delays and impulsive effects via output coupling with delay feedback. Math Comput Model 52:643–653MATHMathSciNetCrossRef
23.
go back to reference Ding S, Wang Z (2015) Stochastic exponential synchronization control of memristive neural networks with multiple time-varying delays. Neurocomputing 162:16–25CrossRef Ding S, Wang Z (2015) Stochastic exponential synchronization control of memristive neural networks with multiple time-varying delays. Neurocomputing 162:16–25CrossRef
24.
go back to reference Zhang G, Hu J, Shen Y (2015) Exponential lag synchronization for delayed memristive recurrent neural networks. Neurocomputing 154:86–93CrossRef Zhang G, Hu J, Shen Y (2015) Exponential lag synchronization for delayed memristive recurrent neural networks. Neurocomputing 154:86–93CrossRef
25.
go back to reference Zhang G, Shen Y (2015) Exponential stabilization of memristor-based chaotic neural networks with time-varying delays via intermittent control. IEEE Trans Neural Netw Learn Syst 26:1431–1441CrossRef Zhang G, Shen Y (2015) Exponential stabilization of memristor-based chaotic neural networks with time-varying delays via intermittent control. IEEE Trans Neural Netw Learn Syst 26:1431–1441CrossRef
26.
go back to reference Bao H, Cao J (2015) Projective synchronization of fractional-order memristor-based neural networks. Neural Netw 63:1–9CrossRef Bao H, Cao J (2015) Projective synchronization of fractional-order memristor-based neural networks. Neural Netw 63:1–9CrossRef
27.
28.
go back to reference Fridman E, Seuret A, Richard J (2004) Robust sampled-data stabilization of linear systems: an input delay approach. Automatica 40:1441–1446MATHMathSciNetCrossRef Fridman E, Seuret A, Richard J (2004) Robust sampled-data stabilization of linear systems: an input delay approach. Automatica 40:1441–1446MATHMathSciNetCrossRef
29.
go back to reference Boyd S, Ghaoui L, Feron E, Balakrishnan V (1994) Linear matrix inequalities in system and control theory. SIAM, PhiladephiaMATHCrossRef Boyd S, Ghaoui L, Feron E, Balakrishnan V (1994) Linear matrix inequalities in system and control theory. SIAM, PhiladephiaMATHCrossRef
30.
go back to reference Lu J (2008) Global exponential stability and periodicity of reaction-diffusion delayed recurrent neural networks with Dirichlet boundary conditions. Chaos Solitons Fract 35:116–125MATHCrossRef Lu J (2008) Global exponential stability and periodicity of reaction-diffusion delayed recurrent neural networks with Dirichlet boundary conditions. Chaos Solitons Fract 35:116–125MATHCrossRef
Metadata
Title
Synchronization of delayed Markovian jump memristive neural networks with reaction–diffusion terms via sampled data control
Authors
Ruoxia Li
Hongzhi Wei
Publication date
01-02-2016
Publisher
Springer Berlin Heidelberg
Published in
International Journal of Machine Learning and Cybernetics / Issue 1/2016
Print ISSN: 1868-8071
Electronic ISSN: 1868-808X
DOI
https://doi.org/10.1007/s13042-015-0423-9

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