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Finite-Time Synchronization of Complex-Valued Neural Networks with Mixed Delays and Uncertain Perturbations

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Abstract

This paper concerns the problem of finite-time synchronization for a class of complex-valued neural networks (CVNNs) with both time-varying and infinite-time distributed delays (mixed delays). Both the driving and response CVNNs are disturbed by external uncertain perturbations, which may be nonidentical. A simple state-feedback controller is designed such that the response CVNNs can be synchronized with the driving system in a settling time. By using inequality techniques and constructing some new Lyapunov–Krasovskii functionals, several sufficient conditions are derived to ensure the synchronization. It is discovered that the settling time cannot be estimated when the interested CVNNs exhibit infinite-time distributed delays, while it can be explicitly estimated for the CVNNs with bounded delays. The settling time is dependent on both the delays and the initial value of the error system. Finally, numerical simulations demonstrate the effectiveness of the theoretical results.

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References

  1. Li C, Liao X, Wong K (2004) Chaotic lag synchronization of coupled time-delayed systems and its applications in secure communication. Phys D Nonlinear Phenom 194:187–202

    Article  MathSciNet  MATH  Google Scholar 

  2. Yang X, Yang Z, Nie X (2014) Exponential synchronization of discontinuous chaotic systems via delayed impulsive control and its application to secure communication. Commun Nonlinear Sci Numer Simul 19:1529–1543

    Article  MathSciNet  Google Scholar 

  3. Xie Q, Chen G, Bollt EM (2002) Hybrid chaos synchronization and its application in information processing. Math Comput Model 35:145–163

    Article  MathSciNet  MATH  Google Scholar 

  4. Tan Z, Ali MK (2001) Associative memory using synchronization in a chaotic neural network. Int J Mod Phys C 12:19–29

    Article  Google Scholar 

  5. Hoppensteadt FC, Izhikevich EM (2000) Pattern recognition via synchronization in phase-locked loop neural networks. IEEE Trans Neural Netw 11:734–738

    Article  Google Scholar 

  6. Che YQ, Wang J, Cui SG, Deng B, Wei XL, Chan WL, Tsang KM (2011) Chaos synchronization of coupled neurons via adaptive sliding mode control. Nonlinear Anal Real World Appl 12:3199–3206

    Article  MathSciNet  MATH  Google Scholar 

  7. Zhang W, Tang Y, Wu X, Fang J (2014) Synchronization of nonlinear dynamical networks with heterogeneous impulses. IEEE Trans Circuits Syst I 61(4):1220–1228

  8. Yang X, Cao J, Qiu J (2015) pth moment exponential stochastic synchronization of coupled memristor-based neural networks with mixed delays via delayed impulsive control. Neural Netw 65:80–91

    Article  Google Scholar 

  9. Feng J, Yu F, Zhao Y (2016) Exponential synchronization of nonlinearly coupled complex networks with hybrid time-varying delays via impulsive control. Nonlinear Dyn 85(1):621–632

    Article  MathSciNet  MATH  Google Scholar 

  10. Yang X, Cao J (2013) Synchronization of discontinuous neural networks with delays via adaptive control. Discrete Dyn Nat Soc. doi:10.1155/2013/147164

  11. Park JH (2009) Synchronization of cellular neural networks of neutral type via dynamic feedback controller. Chaos Solitons Fractals 42:1299–1304

    Article  MathSciNet  MATH  Google Scholar 

  12. Li Q, Guo J, Wu Y, Sun C Weighted average pinning synchronization for a class of coupled neural networks with time-varying delays. Neural Process Lett. doi:10.1007/s11063-016-9514-1

  13. Yang X, Cao J, Ho DWC (2015) Exponential synchronization of discontinuous neural networks with time-varying mixed delays via state feedback and impulsive control. Cogn Neurodyn 9:113–128

    Article  Google Scholar 

  14. Zuo Y, Yang X (2013) Synchronization of coupled networks with uncertainties. Abstr Appl Anal 2013:1–13

    MathSciNet  Google Scholar 

  15. Mei J, Jiang M, Wang B et al (2014) Exponential p-synchronization of non-autonomous Cohen–Grossberg neural networks with reaction-diffusion terms via periodically intermittent control. Neural Process Lett 40:103–126

    Article  Google Scholar 

  16. Shi Y, Zhu P (2013) Adaptive synchronization of different Cohen–Grossberg chaotic neural networks with unknown parameters and time-varying delays. Nonlinear Dyn 73:1721–1728

    Article  MathSciNet  MATH  Google Scholar 

  17. Kao Y, Wang C, Zhang L (2013) Delay-dependent exponential stability of impulsive Markovian jumping Cohen–Grossberg neural networks with reaction-diffusion and mixed delays. Neural Process Lett 38:321–346

    Article  Google Scholar 

  18. Ling G, Nian X, Pan H (2012) Synchronization of perturbed chaotic systems via nonlinear control. J Cent South Univ 19:2803–2809

    Article  Google Scholar 

  19. Zhang Q (2014) Robust synchronization of FitzHugh–Nagumo network with parameter disturbances by sliding mode control. Chaos Solitons Fractals 58:22–26

    Article  MathSciNet  MATH  Google Scholar 

  20. Zheng C, Cao J (2014) Robust synchronization of coupled neural networks with mixed delays and uncertain parameters by intermittent pinning control. Neurocomputing 141:153–159

    Article  Google Scholar 

  21. Wu E, Yang X (2016) Adaptive synchronization of coupled nonidentical chaotic systems with complex variables and stochastic perturbations. Nonlinear Dyn 84(1):261–269

    Article  MathSciNet  MATH  Google Scholar 

  22. Shen Y, Miao P, Huang Y, Shen Y (2015) Finite-time stability and its application for solving time-varying Sylvester equation by recurrent neural network. Neural Process Lett 42:763–784

    Article  Google Scholar 

  23. Shi L, Yang X, Li Y, Feng Z (2015) Finite-time synchronization of nonidentical chaotic systems with multiple time-varying delays and bounded perturbations. Nonlinear Dyn 83:75–87

    Article  MathSciNet  MATH  Google Scholar 

  24. 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 

  25. Huang J, Li C, Huang T, He X (2014) Finite-time lag synchronization of delayed neural networks. Neurocomputing 139:145–149

    Article  Google Scholar 

  26. Hu C, Jiang H, Yu J (2014) Finite-time synchronization of delayed neural networks with Cohen–Grossberg type based on delayed feedback control. Neurocomputing 143:90–96

    Article  Google Scholar 

  27. Yang X (2014) Can neural networks with arbitrary delays be finite-timely synchronized? Neurocomputing 143:275–281

    Article  Google Scholar 

  28. Yang X, Song Q, Liang J, He B (2015) Finite-time synchronization of coupled discontinuous neural networks with mixed delays and nonidentical perturbations. J Franklin Inst 352:4382–4406

    Article  MathSciNet  Google Scholar 

  29. Yang X, Ho DWC, Lu J, Song Q (2015) Finite-time cluster synchronization of T–S fuzzy complex networks with discontinuous subsystems and random coupling delays. IEEE Trans Fuzzy Syst 23(6):2302–2316

    Article  Google Scholar 

  30. Yang X, Lu J (2016) Finite-time synchronization of coupled networks with markovian topology and impulsive effects. IEEE Trans Autom Control 61(8):2256–2261

    Article  MathSciNet  MATH  Google Scholar 

  31. Efimov D, Polyakov A, Fridman E, Perruquetti W, Richard J-P (2014) Comments on finite-time stability of time-delay systems. Automatica 50:1944–1947

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  33. Rauh A, Hannibal L, Abraham NB (1996) Global stability properties of the complex Lorenz model. Phys D 99:45–58

    Article  MathSciNet  MATH  Google Scholar 

  34. Gibbon JD, Mcguinness MJ (1982) The real and complex Lorenz equations in rotating fluids and lasers. Phys D 5:108–122

    Article  MathSciNet  MATH  Google Scholar 

  35. Ning C, Haken H (1990) Detuned lasers and the complex Lorenz equations: subcritical and supercritical Hopf bifurcations. Phys Rev A 41:3826–3837

    Article  Google Scholar 

  36. Dong D, Petersen IR (2009) Quantum control theory and applications: a survey. IET Control Theory Appl 4:2651–2671

    Article  MathSciNet  Google Scholar 

  37. Yang CD (2009) Stability and quantization of complex-valued nonlinear quantum systems. Chaos Solitons Fractals 42:711–723

    Article  MathSciNet  MATH  Google Scholar 

  38. Zhang Z, Lin C, Chen B (2014) Global stability criterion for delayed complex-valued recurrent neural networks. IEEE Trans Neural Netw Learn Syst 25:1704–1708

    Article  Google Scholar 

  39. Chen X, Song Q (2013) Global stability of complex-valued neural networks with both leakage time delay and discrete time delay on times cales. Neurocomputing 121:254–264

    Article  Google Scholar 

  40. Savitha R, Suresh S, Sundararajan N, Saratchandran P (2009) A new learning algorithm with logarithmic performance index for complex-valued neural networks. Neurocomputing 72:3771–3781

    Article  Google Scholar 

  41. Doering CR, Gibbon JD, Holm DD, Nicolaenko B (1988) Low-dimensional behaviour in the complex Ginzburg–Landau equation. Nonlinearity 1:279–309

    Article  MathSciNet  MATH  Google Scholar 

  42. Orszag SA (1971) Accurate solution of the Orr–Sommerfeld stability equation. J Fluid Mech 50:689–703

    Article  MATH  Google Scholar 

  43. Rb M (1977) Geometrical approach to the study of the Riccati differential equation with complex-valued coefficients. J Differ Equ 25:108–114

    Article  MathSciNet  Google Scholar 

  44. Hu J, Wang J (2012) Global stability of complex-valued recurrent neural networks with time-delays. IEEE Trans Neural Netw Learn Syst 23:853–865

    Article  Google Scholar 

  45. Zhou B, Song Q (2013) Boundedness and complete stability of complex-valued neural networks with time delay. IEEE Trans Neural Netw Learn Syst 24:1227–1238

    Article  Google Scholar 

  46. Fang T, Sun J (2014) Stability of complex-valued recurrent neural networks with time-delays. IEEE Trans Neural Netw Learn Syst 25:1709–1713

    Article  Google Scholar 

  47. Xu X, Zhang J, Shi J (2014) Exponential stability of complex-valued neural networks with mixed delays. Neurocomputing 128:483–490

    Article  Google Scholar 

  48. Song Q, Zhao Z, Liu Y (2015) Stability analysis of complex-valued neural networks with probabilistic time-varying delays. Neurocomputing 159:96–104

    Article  Google Scholar 

  49. Wu Z, Chen G, Fu X (2012) Synchronization of a network coupled with complex-variable chaotic systems. Chaos 22:023127

    Article  MathSciNet  MATH  Google Scholar 

  50. Wu Z, Liu D, Ye Q (2015) Pinning impulsive synchronization of complex-variable dynamical network. Commun Nonlinear Sci Numer Simul 20:273–280

    Article  MathSciNet  MATH  Google Scholar 

Download references

Acknowledgements

This work is supported by the National Natural Science Foundation of China (NSFC) under Grant Nos. 61673078, 61472257, and 61273220.

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Authors and Affiliations

  1. Department of Mathematics, Chongqing Normal University, Chongqing, 401331, China

    Chao Zhou & Xinsong Yang

  2. College of Electronic and Information Engineering, Southwest University, Chongqing, 400715, China

    Wanli Zhang

  3. College of Mathematics and Statistics, Shenzhen University, Shenzhen, 518060, China

    Chen Xu & Jianwen Feng

Authors
  1. Chao Zhou
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  2. Wanli Zhang
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  3. Xinsong Yang
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  4. Chen Xu
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  5. Jianwen Feng
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Corresponding author

Correspondence to Xinsong Yang.

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Zhou, C., Zhang, W., Yang, X. et al. Finite-Time Synchronization of Complex-Valued Neural Networks with Mixed Delays and Uncertain Perturbations. Neural Process Lett 46, 271–291 (2017). https://doi.org/10.1007/s11063-017-9590-x

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