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Finite-time synchronization of delayed competitive neural networks with discontinuous neuron activations

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Abstract

This paper is concerned with the finite-time synchronization problem for a class of delayed competitive neural networks with discontinuous activations. Using the theory of differential inclusions, nonsmooth analysis, inequality techniques and a generalized finite-time convergence theorem, new criteria are established to ensure the finite-time stability of the considered error system, and thus the finite-time synchronization between the drive system and the response system are realized. Finally, two examples with numerical simulations are presented to illustrate the effectiveness of the proposed synchronization criteria.

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References

  1. Hopfield JJ, Tank DW (1984) Neurons with graded response have collective computational properties like those of two-state neurons. Proc Nat Acad Sci 79:3088–3092

    Article  MATH  Google Scholar 

  2. Forti M, Nistri P (2003) Global convergence of neural networks with discontinuous neuron activations. IEEE Trans Circuits Syst I(50):1421–1435

    Article  MathSciNet  MATH  Google Scholar 

  3. Hunt KJ, Sbarbaro D, Żbikowski R, Gawthrop PJ (1992) Neural networks for control systems—a survey. Automatica 28:1083–1112

    Article  MathSciNet  MATH  Google Scholar 

  4. 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 

  5. Lu W, Chen T (2006) Dynamical behaviors of delayed neural network systems with discontinuous activation functions. Neural Comput 18:683–708

    Article  MathSciNet  MATH  Google Scholar 

  6. Forti M, Nistri P, Papini D (2005) Global exponential stability and global convergence infinite time of delayed neural networks with infinite gain. IEEE Trans Neural Netw 16:1449–1463

    Article  Google Scholar 

  7. Forti M, Grazzini M, Nistri P, Pancioni L (2006) Generalized Lyapunov approach for convergence of neural networks with discontinuous or non-Lipschitz activations. Phys D 214:88–99

    Article  MathSciNet  MATH  Google Scholar 

  8. Papini D, Taddei V (2005) Global exponential stability of the periodic solution of a delayed neural network with discontinuous activations. Phys Lett A 343:117–128

    Article  MATH  Google Scholar 

  9. Liu X, Cao J (2010) Robust state estimation for neural networks with discontinuous activations. IEEE Trans Syst Man Cybern 40:1425–1437

    Article  Google Scholar 

  10. Duan L, Huang L, Guo Z (2014) Stability and almost periodicity for delayed high-order Hopfield neural networks with discontinuous activations. Nonlinear Dyn 77:1469–1484

    Article  MathSciNet  MATH  Google Scholar 

  11. Liu J, Liu X, Xie W (2012) Global convergence of neural networks with mixed time-varying delays and discontinuous neuron activations. Inform Sci 183:92–105

    Article  MathSciNet  MATH  Google Scholar 

  12. Duan L, Huang L, Guo Z (2016) Global robust dissipativity of interval recurrent neural networks with time-varying delay and discontinuous activations. Chaos 26:073101

    Article  MathSciNet  MATH  Google Scholar 

  13. Meyer-Bäse A, Ohl F, Scheich H (1996) Singular perturbation analysis of competitive neural networks with different time scales. Neural Comput 8:1731–1742

    Article  Google Scholar 

  14. Meyer-Bäse A, Botella G, Rybarska-Rusinek L (2013) Stochastic stability analysis of competitive neural networks with different time-scales. Neurocomputing 118:115–118

    Article  Google Scholar 

  15. Nie X, Cao J (2009) Multistability of competitive neural networks with time-varying and distributed delays. Nonlinear Anal Real World Appl 10:928–942

    Article  MathSciNet  MATH  Google Scholar 

  16. Engel PM, Molz RF (1998) A new proposal for implementation of competitive neural networks in analog hardware. In: Proceedings of the 5th Brazilian Symposium on Neural Networks, pp 186–191

  17. Lou X, Cui B (2007) Synchronization of competitive neural networks with different time scales. Phys A 380:563–576

    Article  Google Scholar 

  18. Gu H (2009) Adaptive synchronization for competitive neural networks with different time scales and stochastic perturbation. Neurocomputing 73:350–356

    Article  Google Scholar 

  19. Gan Q, Hu R, Liang Y (2012) Adaptive synchronization for stochastic competitive neural networks with mixed time-varying delays. Commun Nonlinear Sci Numer Simul 17:3708–3718

    Article  MathSciNet  MATH  Google Scholar 

  20. Li Y, Yang X, Shi L (2016) Finite-time synchronization for competitive neural networks with mixed delays and non-identical perturbations. Neurocomputing 185:242–253

    Article  Google Scholar 

  21. Cortés J (2008) Discontinuous dynamical systems: a tutorial on solutions, nonsmooth analysis, and stability. IEEE Control Syst Mag. 28:36–73

    MathSciNet  Google Scholar 

  22. Filippov A (1988) Differential equations with discontinuous righthand sides. Kluwer Academic Publishers, Dordrecht

    Book  Google Scholar 

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

    MATH  Google Scholar 

  24. Kisielewicz M (1991) Differential inclusions and optimal control, mathematics and its applications. Kluwer Academic Publishers, Dordrecht

    MATH  Google Scholar 

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

    Article  Google Scholar 

  26. Wang H, Zhu Q (2015) Finite-time stabilization of high-order stochastic nonlinear systems in strict-feedback form. Automatica 54:284–291

    Article  MathSciNet  MATH  Google Scholar 

  27. Shi L, Yang X, Li Y, Feng Z (2016) 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 

  28. Liu X, Chen T, Cao J, Lu W (2011) Dissipativity and quasi-synchronization for neural networks with discontinuous activations and parameter mismatches. Neural Netw 24:1013–1021

    Article  MATH  Google Scholar 

  29. Liu X, Cao J (2011) Local synchronization of one-to-one coupled neural networks with discontinuous activations. Cogn Neurodyn 5:13–20

    Article  Google Scholar 

  30. Shen J, Cao J (2011) Finite-time synchronization of coupled neural networks via discontinuous controllers. Cogn Neurodyn 5:373–385

    Article  Google Scholar 

  31. 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 

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

    Article  MathSciNet  MATH  Google Scholar 

  33. Zhang H, Wang J, Wang Z, Liang H (2015) Mode-dependent stochastic dynchronization for markovian coupled neural networks with time-varying mode-delays. IEEE Trans Neural Netw Learn Syst 26:2631–2634

    Google Scholar 

  34. Pan Y, Yu H, Er MJ (2014) Adaptive neural PD control with semiglobal asymptotic stabilization guarantee. IEEE Trans Neural Netw Learn Syst 25:2264–2274

    Article  Google Scholar 

  35. Pan Y, Liu Y, Xu B, Yu H (2016) Hybrid feedback feedforward: an efficient design of adaptive neural network control. Neural Netw 76:122–134

    Article  Google Scholar 

Download references

Acknowledgements

We would like to thank the editors and the anonymous reviewers for carefully reading the original manuscript and for the constructive comments and suggestions to improve the presentation of this paper.

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Authors and Affiliations

  1. School of Mathematics and Big Data, Anhui University of Science and Technology, Huainan, 232001, Anhui, People’s Republic of China

    Lian Duan & Xianwen Fang

  2. College of Mathematics and Econometrics, Hunan University, Changsha, 410082, Hunan, People’s Republic of China

    Xuejun Yi & Yujie Fu

Authors
  1. Lian Duan
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  2. Xianwen Fang
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  3. Xuejun Yi
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  4. Yujie Fu
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Corresponding author

Correspondence to Xuejun Yi.

Additional information

This work was supported by the National Natural Science Foundation of China (11371127, 61572035, 61170059), Key Program of Scientific Research Fund for Young Teachers of Anhui University of Science and Technology (QN201605), Doctoral Fund of Anhui University of Science and Technology (11668) and the Key Program of University Natural Science Research Fund of Anhui Province (KJ2017A088).

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Duan, L., Fang, X., Yi, X. et al. Finite-time synchronization of delayed competitive neural networks with discontinuous neuron activations. Int. J. Mach. Learn. & Cyber. 9, 1649–1661 (2018). https://doi.org/10.1007/s13042-017-0670-z

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  • DOI: https://doi.org/10.1007/s13042-017-0670-z

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