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Adaptive Synchronization of Stochastic Memristor-Based Neural Networks with Mixed Delays

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Abstract

In this paper, adaptive synchronization of stochastic memristor-based neural networks with mixed delays is investigated. By using the differential inclusions theory, adaptive control technique and stochastic Lyapunov method, two adaptive updated laws are designed and two synchronization criteria are derived for stochastic memristor-based neural networks with mixed delays. The derived criteria complement and improve the previously known results since stochastic perturbations and mixed delays are considered. Finally, two numerical examples are provided to illustrate the effectiveness of the theoretical results.

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References

  1. Chua L (1971) Memristor-the missing circuit element. IEEE Trans Circuit Theory 18:507–519

    Article  Google Scholar 

  2. Strukov D, Snider G, Stewart D, Williams R (2008) The missing memristor found. Nature 453:80–83

    Article  Google Scholar 

  3. Cao J, Lu J (2006) Adaptive synchronization of neural networks with or without time-varying delay. Chaos 16:121–133

    MathSciNet  MATH  Google Scholar 

  4. Zhang H, Huang W, Wang Z, Chai T (2006) Adaptive synchronization between two different chaotic systems with unknown parameters. Phys Lett A 350:363–366

    Article  MATH  Google Scholar 

  5. 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 21:11–25

    Article  Google Scholar 

  6. Liu Y, Wang Z, Liang J, Liu X (2009) Stability and synchronization of discerete-time Markovian jumping neural networks with mixed mode-dependent time delays. IEEE Trans Neural Netw 20:1102–1116

    Article  Google Scholar 

  7. Lu W, Chen T (2004) Synchronization of coupled connected neural networks with delays. IEEE Trans Circuits Syst I Regul Pap 51:2491–2504

    Article  MathSciNet  MATH  Google Scholar 

  8. Shen Y, Wang J (2012) Robust analysis of global exponential stability of recurrent neural networks in the presence of time delays and random disturbances. IEEE Trans Neural Netw Learn Syst 23:87–96

    Article  Google Scholar 

  9. Wang K, Teng Z, Jiang H (2008) Adaptive synchronization of neural networks with time-varying delay and distributed delay. Phys A 387:631–642

    Article  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  11. Zhu Q, Cao J (2011) Adaptive synchronization under almost every initial data for stochastic neural networks with time-varying delays and distributed delays. Commun Nonlinear Sci Numer Simul 16:2139–2159

    Article  MathSciNet  MATH  Google Scholar 

  12. Wu A, Zeng Z, Zhu X, Zhang J (2011) Exponential synchronization of memristor-based recurrent networks with timedelays. Neurocomputing 74:3043–3053

    Article  Google Scholar 

  13. Wu A, Wen S, Zeng Z (2012) Synchronization control of a class of memristor-based recurrent neural networks. Inf Sci 183:106–116

    Article  MathSciNet  MATH  Google Scholar 

  14. Wen S, Gang Bao, Zeng Z, Chen Y, Huang T (2013) Global exponential synchronization of memristor-based recurrent neural networks with time-varying delays. Neural Netw 48:195–203

    Article  MATH  Google Scholar 

  15. Yang X, Cao J, Long Y, Rui W (2010) Adaptive lag synchronization for competitive neural networks with mixed delays and uncertain hybrid perturbations. IEEE Trans Neural Netw 21(10):1656–1667

    Article  Google Scholar 

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

    Article  MATH  Google Scholar 

  17. Li N, Cao J (2015) New synchronization criteria for memristor-based networks: adaptive control and feedback control schemes. Neural Netw 61:1–9

    Article  MATH  Google Scholar 

  18. Wang L, Shen Y, Yin Q, Zhang G (2015) Adaptive synchronization of memristor-based neural networks with time-varying delays. IEEE Trans Neural Netw Learn Syst 24:1701–1707

    MathSciNet  Google Scholar 

  19. Zhang G, Shen Y (2014) Exponential synchronization of delayed memristor-based chaotic neural networks via periodically intermittent control. Neural Netw 55:1–10

    Article  MATH  Google Scholar 

  20. Cai Z, Huang L, Wang D, Zhang L (2015) Periodic synchronization in delayed memristive neural networks based on Filippov systems. J Frankl Inst 352:4638–4663

    Article  MathSciNet  Google Scholar 

  21. Guo Z, Wang J, Yan Z (2014) Passivity and passification of memristor-based recurrent neural networks with time-varying delays. IEEE Trans Neural Netw Learn Syst 25:2099–2109

    Article  Google Scholar 

  22. Zhang W, Li C, Huang T, Huang J (2016) Stability and synchronization of memristor-based coupling neural networks with time-varying delays via intermittent control. Neurocomputing 173:1066–1072

    Article  Google Scholar 

  23. Abdurahman A, Jiang H, Teng Z (2015) Finite-time synchronization for memristor-based neural networks with time-varying delays. Neural Netw 63:1–9

    Article  Google Scholar 

  24. Bao H, Park JH, Cao J (2016) Matrix measure strategies for exponential synchronization and anti-synchronization of memristor-based neural networks with time-varying delays. Appl Math Comput 142:143–154

    Google Scholar 

  25. Wang W, Peng H, Li L, Xiao J, Yang J (2013) Finite-time function projective synchronization in complex multi-links networks with time-varying delay. Neural Process Lett. doi:10.1007/s11063-013-9335-4

  26. Wu H, Li R, Zhang X, Yao R (2015) Adaptive finite-time complete periodic synchronization of memristive neural networks with time delays. Neural Process Lett. doi:10.1007//s11063-014-9373-6

  27. Abdurahman A, Jiang H, Rahman K (2015) Function projective synchronization of memristor-based Cohen–Grossberg neural networks with time-varying delays. Cogn Neurodyn 9:603–613

    Article  Google Scholar 

  28. Du H, Wen G, Chen Y, He Y, Jia R (2016) Distributed finite-time cooperative control of multiple high-order nonholonomic mobile robots. IEEE Trans Neural Netw Learn Syst. doi:10.1109/TNNLS.2016.2610140

  29. Du H, Li S (2016) Attitude synchronization for flexible spacecraft with communication delays. IEEE Trans Autom Control 61(11):3625–3630

    Article  MathSciNet  MATH  Google Scholar 

  30. Du H, Li S, Qian C (2011) Finite-time attitude tracking control of spacecraft with application to attitude synchronization. IEEE Trans Autom Control 56(11):2711–2717

    Article  MathSciNet  MATH  Google Scholar 

  31. Li S, Du H, Lin X (2011) Finite time consensus algorithm for multi-agent systems with double integrator dynamics. Automatica 47(8):1706–1712

    Article  MathSciNet  MATH  Google Scholar 

  32. Haykin S (1994) Neural networks: a comprehensive foundation. Prentice Hall, New Jersey

    MATH  Google Scholar 

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

    Article  Google Scholar 

  34. Ding S, Wang Z (2015) Stochastic exponential synchronization control of memristive neural networks with multiple time-varying delays. Neurocomputing 162:16–25

    Article  Google Scholar 

  35. 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 

  36. Chandrasekar A, Rakkiyappan R (2016) Impulsive controller design for exponential synchronization of delayed stochastic memristor-based recurrent neural networks. Nerocomputing 173:1348–1355

    Article  Google Scholar 

  37. Wang W, Li L, Peng H, Kurths J, Xiao J, Yang Y (2014) Finite-time anty-synchronization control of memrsitive neural networks with stochastic perturbations. Neural Process Lett. doi:10.1007/s11063-014-9401-6

  38. Zhao H, Li L, Peng H, Kurths J, Xiao J, Yang Y (2015) Anti-synchronization for stochastic memristor-based neural networks with non-modeled dynamics via adaptive control approach. Eur Phys J B 88:2–10

  39. Yang X, Cao J (2014) Hybrid adaptive and impulsive synchronization of uncertain complex networks with delays and general uncertain perturbations. Apple Math Comput 227(15):480–493

    Article  MathSciNet  MATH  Google Scholar 

  40. Yang X, Cao J, Yu W (2014) Exponential synchronization of memristive Cohen–Grossberg neural networks with mixed delays. Cogn Neurodyn 8:239–249

    Article  Google Scholar 

  41. Yang X, Ho DWC (2015) Synchronization of delayed memristive neural networks: robust analysis approach. IEEE Trans Cybern. doi:10.1109/TCYB.2015.2505903

  42. Yang X, Cao J, Liang J (2016) Exponential synchronization of memristive neural networks with delays: interval matrix method. IEEE Trans Neural Netw Learn Syst. doi:10.1109/TNNLS.2016.2561298

  43. Chandrasekar A, Rakkiyappan R, Cao J, Lakshmanan S (2014) Synchronization of memristor-based recurrent neural networks with two delay components based on second-order reciprocally convex approach. Neural Netw 57:79–93

    Article  MATH  Google Scholar 

  44. Rakkiyappan R, Chandrasekar A, Cao J (2015) Passivity and passification of memristor-based recurrent neural networks with additive time-varying delays. IEEE Trans Neural Netw 26(9):2043–2057

    Article  MathSciNet  Google Scholar 

  45. Rakkiyappan R, Velmurugan G, Cao J (2015) Stability analysis of memristor-based fractional-order neural networks with different memductance functions. Cognit Neurodyn 9:145–177

    Article  Google Scholar 

  46. Velmurugan G, Rakkiyappan R, Cao J (2016) Finite-time synchronization of fractional-order memristor-based neural networks with time delays. Neural Netw 73:36–46

    Article  MATH  Google Scholar 

  47. Lu J (2012) Pinning impulsive stabilization of nonlinear dynamical networks with time-varying delay. Int J Bifurc Chaos 22(7):1250176

    Article  MATH  Google Scholar 

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

    Article  MATH  Google Scholar 

Download references

Acknowledgements

This work was supported by the National Natural Science Foundation of China under Grant 61503046 and 11547006. The authors thank the anonymous editor and reviewers for a number of constructive comments and suggestions that have improved the quality of the paper.

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Correspondence to Yinfang Song.

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Song, Y., Sun, W. Adaptive Synchronization of Stochastic Memristor-Based Neural Networks with Mixed Delays. Neural Process Lett 46, 969–990 (2017). https://doi.org/10.1007/s11063-017-9623-5

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