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.







Similar content being viewed by others
Explore related subjects
Discover the latest articles and news from researchers in related subjects, suggested using machine learning.References
Chua L (1971) Memristor—the missing circuit element. IEEE Trans Circuit Theory 18:507–519
Strukov D, Snider G, Stewart D, Williams R (2008) The missing memristor found. Nature 453:80–83
Corinto F, Ascoli A, Gilli M (2011) Nonlinear dynamics of memristor oscillators. IEEE Trans Circuits Syst I 58:1323–1336
Tour J, He T (2008) Electronics: the fourth element. Nature 453:42–43
Messias M, Nespoli C, Botta V (2010) Hopf bifurcation from lines of equilibria without parameters in memristor oscillators. Int J Bifurcation Chaos 20:437–450
Itoh M, Chua L (2008) Memristor oscillators. Int J Bifurcation Chaos 18:3183–3206
Petras I (2010) Fractional-order memristor-based Chua’s circuit. IEEE Trans Circuits Syst II Exp Briefs 57:975–979
Tsang E, Wang X, Yeung D (2000) Improving learning accuracy of fuzzy decision trees by hybrid neural networks. IEEE Trans Fuzzy Syst 8:601–614
Wang X, Dong C, Fan T (2007) Training T-S norm neural networks to refine weights for fuzzy if-then rules. Neurocomputing 70:2581–2587
Roska T, Chua L (1992) Cellular neural networks with nonlinear and delay-type tempiate. Int J Circuit Theory Appl 20:469–481
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 39:94–102
Wang Z, Liu Y, Yu L, Liu X (2006) Exponential stability of delayed recurrent neural networks with Markovian jumping parameters. Phys Lett A 356:346–352
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 22:1566–1575
Zhang H, Wang Y (2008) Stability analisis of Markovian jumping stochastic Cohen–Grossberg neural networks with mixed time delays. IEEE Trans Neural Netw 19:366–370
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
Landsman A, Schwartz I (2007) Complete chaotic synchronization in mutually coupled time-delay systems. Phys Rev E 5:26–33
Huang T, Li C, Liao X (2007) Synchronization of a class of coupled chaotic delays systems with parameter mismatch. Chaos 17:33–121
Cui B, Lou X (2009) Synchronization of chaotic recurrent neural networks with time-varying delays using nonlinear feedback control. Chaos Solitons Fract 39:288–294
Gan Q, Xu R, Kang X (2011) Synchronization of chaotic neural networks with mixed time delays. Commun Nonlinear Sci Numer Simul 16:966–974
Zhan M, Wei G, Lai C (2002) Transition from intermittency to periodicity in lag synchronization in coupled Rössler oscillators. Phys Rev E 65:36–40
Xu D, Chee C (2002) Controlling the ultimate state of projective synchronization in chaotic systems of arbitrary dimension. Phys Rev E 66:46–50
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 52:643–653
Ding S, Wang Z (2015) Stochastic exponential synchronization control of memristive neural networks with multiple time-varying delays. Neurocomputing 162:16–25
Zhang G, Hu J, Shen Y (2015) Exponential lag synchronization for delayed memristive recurrent neural networks. Neurocomputing 154:86–93
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 26:1431–1441
Bao H, Cao J (2015) Projective synchronization of fractional-order memristor-based neural networks. Neural Netw 63:1–9
Wu A, Wen S, Zeng Z (2012) Synchronization control of a class of memristor-based recurrent neural networks. Inf Sci 183:106–116
Fridman E, Seuret A, Richard J (2004) Robust sampled-data stabilization of linear systems: an input delay approach. Automatica 40:1441–1446
Boyd S, Ghaoui L, Feron E, Balakrishnan V (1994) Linear matrix inequalities in system and control theory. SIAM, Philadephia
Lu J (2008) Global exponential stability and periodicity of reaction-diffusion delayed recurrent neural networks with Dirichlet boundary conditions. Chaos Solitons Fract 35:116–125
Acknowledgments
This work was supported by the Scientific and Technological Research Program of Chongqing Municipal Education Commission (Grant No. KJ1501002).
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Li, R., Wei, H. Synchronization of delayed Markovian jump memristive neural networks with reaction–diffusion terms via sampled data control. Int. J. Mach. Learn. & Cyber. 7, 157–169 (2016). https://doi.org/10.1007/s13042-015-0423-9
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s13042-015-0423-9