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Synchronization analysis for coupled static neural networks with stochastic disturbance and interval time-varying delay

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Abstract

This paper is concerned with the stochastic synchronization problem of coupled static neural networks with interval time-varying delays. By employing the augmented Lyapunov–Krasovskii method and a new method to deal with the Kronecker product, a delay-dependent synchronization criterion is established to guarantee the global asymptotical mean-square synchronization of the addressed delayed networks with stochastic disturbances. The obtained result is formulated in terms of linear matrix inequalities which can be easily checked. Finally, two numerical examples are provided to illustrate the effectiveness of the proposed results.

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References

  1. Zhang H, Wang Z, Liu D (2014) A comprehensive review of stability analysis of continuous-time recurrent neural networks. IEEE Trans Neural Netw Learn Syst 25(7):1229–1262

    Article  Google Scholar 

  2. Fuchs E, Gruber C, Reitmaier T, Sick B (2009) Processing short-term and long-term information with a combination of polynomial approximation techniques and time-delay neural networks. IEEE Trans Neural Netw 20(9):1450–1462

    Article  Google Scholar 

  3. Majidi M, Fadali MS, Etezadi-Amoli M, Oskuoee M (2015) Partial discharge pattern recognition via sparse representation and ANN. IEEE Trans Dielectr Electr Insul 22(2):1061–1070

    Article  Google Scholar 

  4. Zhang H, Cui L, Zhang X, Luo Y (2011) Data-driven robust approximate optimal tracking control for unknown general nonlinear systems using adaptive dynamic programming method. IEEE Trans Neural Netw 22(12):2226–2236

    Article  Google Scholar 

  5. Andonie R et al (2006) An efficient concurrent implementation of a neural network algorithm. Concurr Comput: Pract Exp 18(12):1559–1573

    Article  Google Scholar 

  6. Chronopoulos AT, Jagannathan S (2002) A distributed discrete-time neural network architecture for pattern allocation and control. Proceedings of IEEE IPDPS, pp 204–211

  7. Bertschinger N, Natschlager T (2004) Real-time computation at the edge of chaos in recurrent neural networks. Neural Comput 16(7):1413–1436

    Article  MATH  Google Scholar 

  8. Cao J, Xiao M (2007) Stability and Hopf bifurcation in a simplified BAM neural network with two time delays. IEEE Trans Neural Netw 18(2):416–430

    Article  MathSciNet  Google Scholar 

  9. Liao X, Wu Z, Yu J (1999) Stability switches and bifurcation analysis of a neural network with continuously delay. IEEE Trans Syst Man Cybern Part A: Syst Hum 29(6):692–696

    Article  Google Scholar 

  10. Wang Z, Zhang H (2013) Synchronization stability in complex interconnected neural networks with nonsymmetric coupling. Neurocomputing 108(5):84–92

    Article  Google Scholar 

  11. Zhang H, Gong D, Chen B, Liu Z (2012) Synchronization for coupled neural networks with interval delay: a novel augmented Lyapunov–Krasovskii functional method. IEEE Trans Neural Netw Learn Syst 24(1):58–70

    Article  Google Scholar 

  12. Tang Z, Park JH, Tae LH (2015) Mean square exponential synchronization for impulsive coupled neural networks with time-varying delays and stochastic disturbances. Complexity 21(5):190–202

    Article  MathSciNet  Google Scholar 

  13. Liang J, Wang Z, Liu Y, Liu X (2008) Robust synchronization of an array of coupled stochastic discrete-time delayed neural networks. IEEE Trans Neural Netw 22(2):329–336

    Google Scholar 

  14. Cao J, Wang Z, Sun Y (2007) Synchronization in an array of linearly stochastically coupled networks with time delays. Phys A 385:718–728

    Article  MathSciNet  Google Scholar 

  15. Wang Y, Wang Z, Liang J (2008) A delay fractioning approach to global synchronization of delayed complex networks with stochastic disturbances. Phys Lett A 372(39):6066–6073

    Article  MATH  Google Scholar 

  16. Wang H, Song Q (2011) Synchronization for an array of coupled stochastic discrete-time neural networks with mixed delays. Neurocomputing 74(10):1572–1584

    Article  Google Scholar 

  17. Wang X, Li C, Huang T, Chen L (2014) Impulsive exponential synchronization of randomly coupled neural networks with Markovian jumping and mixed model-dependent time delays. Neural Netw 60(2):25–32

    Article  MATH  Google Scholar 

  18. Song Y, Wen S (2015) Synchronization control of stochastic memristor-based neural networks with mixed delays. Neurocomputing 156(5):121–128

    Article  Google Scholar 

  19. Song B, Park JH, Zheng GW, Zhang Y (2012) Global synchronization of stochastic delayed complex networks. Nonlinear Dyn 70(1):2389–2399

    Article  MathSciNet  MATH  Google Scholar 

  20. Yang X, Cao J, Qiu J (2015) \(p{th}\) moment exponential stochastic synchronization of coupled memristor-based neural networks with mixed delays via delayed impulsive control. Neural Netw 65(5):80–91

    Article  Google Scholar 

  21. Xu Z, Qiao H, Peng J, Zhang B (2003) A comparative study of two modeling approaches in neural networks. Neural Netw 17(1):73–85

    Article  MATH  Google Scholar 

  22. Liu Y, Wang Z, Serrano A, Liu X (2007) Discrete-time recurrent neural networks with time-varying delays: exponential stability analysis. Phys Lett A 362:480–488

    Article  Google Scholar 

  23. Wang Z, Wang Y, Liu Y (2010) Global synchronization for discrete-time stochastic complex networks with randomly occurred nonlinearities and mixed time delays. IEEE Trans Neural Netw 21(1):11–25

    Article  MathSciNet  Google Scholar 

  24. Langville AN, Stewart WJ (2004) The Kronecker product and stochastic automata networks. J Comput Appl Math 167(2):429–447

    Article  MathSciNet  MATH  Google Scholar 

  25. Mao X (2002) Exponential stability of stochastic delay interval systems with Markovian switching. IEEE Trans Autom Control 47:1604–1612

    Article  MathSciNet  MATH  Google Scholar 

  26. Li H, Wong W, Tang Y (2012) Global synchronization stability for stochastic complex dynamical networks with probabilistic interval time-varying delays. J Optim Theory Appl 152:496–516

    Article  MathSciNet  MATH  Google Scholar 

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (61433004, 61603085), Natural Science Foundation of Liaoning Province of China (201601020), the China Postdoctoral Science Foundation (2015M570253) and the Fundamental Research Funds for the Central Universities (N150403004).

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Authors and Affiliations

  1. College of Information Science and Engineering, Northeastern University, Box 134, Shenyang, 110819, China

    Yushuai Li, Bonan Huang & Huaguang Zhang

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  1. Yushuai Li
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  2. Bonan Huang
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  3. Huaguang Zhang
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Correspondence to Bonan Huang.

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Li, Y., Huang, B. & Zhang, H. Synchronization analysis for coupled static neural networks with stochastic disturbance and interval time-varying delay. Neural Comput & Applic 30, 1123–1132 (2018). https://doi.org/10.1007/s00521-016-2724-7

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  • DOI: https://doi.org/10.1007/s00521-016-2724-7

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