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Finite-time synchronization of chaotic neural networks with mixed time-varying delays and stochastic disturbance

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Abstract

This paper treats of the finite-time stochastic synchronization problem of chaotic dynamic neural networks with mixed time-varying delays and stochastic disturbance. State feedback controller and adaptive controller are designed such that the response system can be finite-timely synchronized with corresponding drive system. Some novel and useful finite-time synchronization criteria are derived based on finite-time stability theory. A numerical example presents the effectiveness of our proposed methods.

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References

  1. Balasubramaniam B, Rakkiyappan R (2009) Delay-dependent robust stability analysis of uncertain stochastic neural networks with discrete interval and distributed time-varying delays. Neurocomputing 72:3231–3237

    Article  MATH  Google Scholar 

  2. Chen L, Zhao H (2009) New LMI conditions for global exponential stability of cellular neural networks with delays. Nonlinear Anal 10:287–297

    Article  Google Scholar 

  3. Cao J, Song Q (2006) Stability in Cohen–Grossberg-type bidirectional associative memory neural networks with time-varying delays. Nonlinearity 19:1601–1617

    Article  MathSciNet  MATH  Google Scholar 

  4. Liu B, Huang L (2006) Existence and global exponential stability of periodic solutions for celluar neural networks with time-varying delays. Phys Lett 349:474–483

    Article  Google Scholar 

  5. Pecora LM, Carroll TL (1990) Synchronization in chaotic system 64:821–824

  6. Zhang Q, Lu J, Lv J (2008) Adaptive feedback synchronization of a general complex dynamical network with delayed nodes. IEEE Trans Circuits Syst 55:183–187

    Article  Google Scholar 

  7. Lu J, Ho DWC, Cao J (2010) A unified synchronization criterion for impulsive dynamical networks. Automatica 46:1215–1221

    Article  MathSciNet  MATH  Google Scholar 

  8. Yang X, Cao J, Lu J (2012) Stochastic synchronization of complex networks with nonidentical nodes via hybrid adaptive and impulsive control. IEEE Trans Circuits Syst I Reg Papers 59:371–384

    Article  MathSciNet  Google Scholar 

  9. Lu J, Cao J (2008) Adaptive stabilization and synchronization for chaotic Lur’e systems with time-varying delay. IEEE Trans Circuits Syst I Regular Paper 55:1347–1356

    Article  MathSciNet  Google Scholar 

  10. Yang X, Cao J, Lu J (2013) Synchronization of coupled neural networks with random coupling strengths and mixed probabilistic time-varying delays. Int J Robust Nonlinear Contr 23:2060–2081

    Article  MathSciNet  MATH  Google Scholar 

  11. Gan Q (2012) Adaptive synchronization of Cohen–Grossberg neural networks with unknown parameters and mixed time-varying delays. Commun Nonlinear Sci Numer Simulat 17:3040–3049

    Article  Google Scholar 

  12. Lu J, Cao J (2008) Adaptive synchronization of uncertain dynamical networks with delayed coupling. Nonlinear Dyn 53:107–115

    Article  MathSciNet  MATH  Google Scholar 

  13. Yang X, Cao J, Lu J (2011) Synchronization of delayed complex dynamical networks with impulsive and stochastic effects. Nonlinear Anal Real World Appl 12:2252–2266

    Article  MathSciNet  MATH  Google Scholar 

  14. Lu J, Cao J (2009) Synchronization of a chaotic electronic circuit system with cubic term via adaptive feedback control. Commun Nonlinear Sci Numer Simul 14:3379–3388

    Article  MATH  Google Scholar 

  15. Mei J, Jiang M, Wang J (2013) Finite-time structure identification and synchronization of drive-response systems with uncertain parameter. Commun Nonlinear Sci Numer Simul 18:999–1015

    Article  MathSciNet  MATH  Google Scholar 

  16. Wang T, Zhao S, Zhou W, Yu W (2014) Finite-time master-slave synchronization and parameter identification for uncertain Lurie systems, ISA Transactions

  17. Hu C, Yu J, Jiang H (2014) Finite-time synchronization of delayed neural networks with Cohen–Grossberg type based on delayed feedback control 142:90–96

  18. Mei J, Jiang M, Wang B, Long B (2013) Finite-time parameter identification and adaptive synchronization between two chaotic neural networks 350:1617–1633

  19. Wu Z, Shi P, Su H, Chu J (2012) Exponential synchronization of neural networks with discrete and distributed delays under time-varying sampling. IEEE Trans Neural Netw 23:1368–1376

    Article  Google Scholar 

  20. Zhu Q, Zhou W, Tong D, Fang J (2013) Adaptive synchronization for stochastic neural networks of neutral-type with mixed time-delays. Neurocomputing 99:477–485

    Article  MATH  Google Scholar 

  21. Yang X, Huang C, Zhu Q (2011) Synchronization of switched neural networks with mixed delays via impulsive control. Chaos Solitons Fract 44:817–826

    Article  MathSciNet  MATH  Google Scholar 

  22. Sun Y, Cao J, Wang Z (2007) Exponential synchronization of stochastic perturbed chaotic delayed neural networks. Neurocomputing 70:2465–2477

    Article  Google Scholar 

  23. Li X, Cao J (2008) Adaptive synchronization for delayed neural networks with stochastic perturbation. J Franklin Inst 345:779–791

    Article  MathSciNet  MATH  Google Scholar 

  24. Hassan S, Aria A (2009) Adaptive synchronization of two chaotic systems with stochastic unknown parameters. Commun Nonlinear Sci Numer, Simulat 14

  25. Yang X, Cao J (2010) Finite-time stochastic synchronization of complex networks. Appl Math Model 34:3631–3641

    Article  MathSciNet  MATH  Google Scholar 

  26. Mei J, Jiang M, Xu W, Wang B (2013) Finite-time synchronization control of complex dynamical networks with time delays. Commun Nonlinear Sci Numer Simulat 18:2462–2478

    Article  MathSciNet  MATH  Google Scholar 

  27. Wang W, Zhong S (2012) Stochastic stability analysis of uncertain genetic regulatory networks with mixed time-varying delays. Neurocomputing 82:143–156

    Article  Google Scholar 

  28. Hardy GH, Littlewood JE, Polya G (1988) Inequalities. Cambridge University Press, Cambridge

    Google Scholar 

  29. Cu K (2000) An integral inequality in the stability problem of time delay systems. In: Proceedings of the 39th IEEE conference on decision control, pp 2805–2810

  30. Tang Y (1998) Terminal sliding mode control for rigid robots. Automatica 34:51–56

    Article  MATH  Google Scholar 

  31. Cui W, Sun S, Fang J, Xu Y, Zhao L (2014) Finite-time synchronization of Markovian jump complex networks with partially unknown transition rates. J Franklin Inst 351:2543–2561

    Article  MathSciNet  Google Scholar 

  32. Wang X, Fang J, Mao H, Dai A (2014) Finite-time global synchronization for a class of Markovian jump complex networks with partially unknown transition rates under feedback control. Nonlinear Dyn. doi:10.1007/s11071-014-1644-2

  33. Mei J, Jiang M, Wang X, Han J, Wang S (2014) Finite-time synchronization of drive-response systems via periodically intermittent adaptive control. J Franklin Inst 351:2691–2710

    Article  MathSciNet  Google Scholar 

  34. Mei J, Jiang M, Wu Z, Wang X (2014) Periodically intermittent controlling for finite-time synchronization of complex dynamical networks. Nonlinear Dyn. doi:10.1007/s11071-014-1664-y

  35. Li C, Liao X, Wong K (1999) Chaotic lag synchronization of coupled time-delayed systems and its applications in secure communication. IEEE Trans Neural Netw 10:978–981

    Article  Google Scholar 

  36. Mensour B, Longtin A (1998) Synchronization of delay differential equations with application to private communication. Phys Lett A 244:59–70

    Article  Google Scholar 

  37. Xia Y, Yang Z, Han M (2009) Lag synchronization of unknown chaotic delayed Yang–Yang-type fuzzy neural networks with noise perturbation based on adaptive control and parameter identification. IEEE Trans Neural Netw 20:1165–1180

    Article  Google Scholar 

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Authors and Affiliations

  1. Department of Applied Mathematics, Yanshan University, Qinhuangdao, 066001, China

    Huaiqin Wu, Xiaowei Zhang, Ruoxia Li & Rong Yao

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  1. Huaiqin Wu
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  2. Xiaowei Zhang
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  3. Ruoxia Li
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  4. Rong Yao
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Correspondence to Xiaowei Zhang.

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Wu, H., Zhang, X., Li, R. et al. Finite-time synchronization of chaotic neural networks with mixed time-varying delays and stochastic disturbance. Memetic Comp. 7, 231–240 (2015). https://doi.org/10.1007/s12293-014-0150-x

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  • DOI: https://doi.org/10.1007/s12293-014-0150-x

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