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General Decay Lag Synchronization for Competitive Neural Networks with Constant Delays

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Abstract

This paper is concerned with the general decay lag synchronization problem for a class of competitive neural networks with constant delays via designing a novel nonlinear feedback controller. Based on the useful lemma, which guarantee the general decay synchronization of chaotic systems, some simple sufficient criteria ensuring the general decay lag synchronization of addressed competitive neural networks are obtained via constructing a novel Lyapunov–Krasovskii functional and using some inequality techniques. Finally, one numerical example is provide to demonstrate the feasibility of the established theoretical results. The results of this paper are general since the classical polynomial synchronization and exponential synchronization can be seen the special cases of general decay synchronization.

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References

  1. Nie X, Cao J (2012) Existence and global stability of equilibrium point for delayed competitive neural networks with discontinuous activation functions. Int J Syst Sci 43(3):459–474

    Article  MathSciNet  MATH  Google Scholar 

  2. Nie X, Cao J, Fei S (2013) Multistability and instability of delayed competitive neural networks with nondecreasing piecewise linear activation functions. Neurocomputing 119(16):281–291

    Article  Google Scholar 

  3. Yang X, Cao J (2016) Adaptive lag synchronization for competitive neural networks with mixed delays and uncertain hybrid perturbations. IEEE Trans Neural Netw Learn Syst 185(10):242–253

    Google Scholar 

  4. Li X, Cao J (2006) Adaptive synchronization for delayed neural networks with stochastic perturbation. Phys Lett A 353(4):318–325

    Article  Google Scholar 

  5. Cao J, Lu J (2006) Adaptive synchronization of neural networks with or without timevarying delay. Chaos 16(1):037203

    Google Scholar 

  6. Yang X, Cao J, Long Y, Rui W (2016) Adaptive lag synchronization for competitive neural networks with mixed delays and uncertain hybrid perturbations. IEEE Trans Neural Netw Learn Syst 185(10):242–253

    Google Scholar 

  7. Nie X, Huang Z (2012) Multistability and multiperiodicity of high-order competitive neural networks with a general class of activation functions. Neurocomputing 82(1):1–13

    Article  Google Scholar 

  8. Pecora LM, Carroll TL (1996) Synchronization in chaotic systems. Phys Rev Lett 06(08):142–145

    Google Scholar 

  9. Lu J, Ho DW, Wu L (2009) Exponential stabilization of switched stochastic dynamical networks. Nonlinearity 22:889–911

    Article  MathSciNet  MATH  Google Scholar 

  10. Garcia-Ojalvo J, Roy R (2001) Spatiotemporal communication with synchronized optical chaos. Phys Rev Lett 86(22):5204–5207

    Article  Google Scholar 

  11. Lu J, Ho DW (2011) Stabilization of complex dynamical networks with noise disturbance under performance constraint. Nonlinear Anal Real World Appl 12:1974–1984

    Article  MathSciNet  MATH  Google Scholar 

  12. Li Y, Lou J, Wang Z, Alsaadi FE (2018) Synchronization of nonlinearly coupled dynamical networks under hybrid pinning impulsive controllers. J Frankl Inst 355:6520–6530

    Article  MATH  Google Scholar 

  13. Lu J, Ding C, Lou J, Cao J (2015) Outer synchronization of partially coupled dynamical networks via pinning impulsive controllers. J Frankl Inst 352:5024–5041

    Article  MathSciNet  MATH  Google Scholar 

  14. Shahverdiev EM, Shore KA (2002) Generalized synchronization in time-delayed systems. Phys Lett A 292(6):320–324

    Article  MATH  Google Scholar 

  15. Liang J, Li P, Yang Y (2007) Adaptive lag synchronization ounknown chaotic delayed neural networks with noise perturbation. Phys Lett A 364(3):277–285

    Google Scholar 

  16. Cao Y, Wen S, Huang T (2017) New criteria on exponential lag synchronization of switched neural networks with time-varying delays. Neural Process Lett 46:451–466

    Article  Google Scholar 

  17. Tao Y, Chua LO (2011) Impulsive control and synchronization of nonlinear dynamical systems and application to secure communication. Int J Bifurc Chaos 7(3):645–664

    MathSciNet  MATH  Google Scholar 

  18. Mainieri R, Rehacek J (1999) Projective synchronization in three-dimensional chaotic systems. Phys Rev Lett 82(82):3042–3045

    Article  Google Scholar 

  19. Abdurahman A, Jiang H, Teng Z (2014) Function projective synchronization of impulsive neural networks with mixed time-varying delays. Nonlinear Dyn 78(4):2627–2638

    Article  MathSciNet  MATH  Google Scholar 

  20. Hu C, Yu J, Jiang H, Teng Z (2010) Exponential lag synchronization for neural networks with mixed delays via periodically intermittent control. Chaos 20(2):023108

    Article  MathSciNet  MATH  Google Scholar 

  21. Abdurahman A, Jiang H, Teng Z (2017) Lag synchronization for Cohen–Grossberg neural networks with mixed time-delays via periodically intermittent control. Int J Comput Math 94(2):275–295

    Article  MathSciNet  MATH  Google Scholar 

  22. Yu J, Hu C, Jiang H, Teng Z (2012) Exponential lag synchronization for delayed fuzzy cellular neural networks via periodically intermittent control. Math Comput Simul 82(5):895–908

    Article  MathSciNet  MATH  Google Scholar 

  23. Zhang L, Yang Y, Wang F (2017) Lag synchronization for fractional-order memristive neural networks via period intermittent control. Nonlinear Dyn 3:1–15

    Article  MATH  Google Scholar 

  24. Wen S, Zeng Z, Huang T, Meng Q, Yao W (2015) Lag synchronization of switched neural networks via neural activation function and applications in image encryption. IEEE Trans Neural Netw Learn Syst 26(7):1493–1502

    Article  MathSciNet  Google Scholar 

  25. Zhou P, Cai S (2018) Adaptive exponential lag synchronization for neural networks with mixed delays via intermittent control. Adv Differ Equ 2018(1):40

    Article  MathSciNet  MATH  Google Scholar 

  26. Hien LV, Phat VN, Trinh H (2015) New generalized halanay inequalities with applications to stability of nonlinear non-autonomous time-delay systems. Nonlinear Dyn 82:1–13

    Article  MathSciNet  MATH  Google Scholar 

  27. Wang L, Shen Y, Zhang G (2016) General decay synchronization stability for a class of delayed chaotic neural networks with discontinuous activations. Neurocomputing 179:169–175

    Article  Google Scholar 

  28. Abdurahman A (2018) New results on the general decay synchronization of delayed neural networks with general activation functions. Neurocomputing 275:2505–2511

    Article  Google Scholar 

  29. Abdurahman A, Jiang H, Hu C (2017) General decay synchronization of memristorbased Cohen–Grossberg neural networks with mixed time-delays and discontinuous activations. J Frankl Inst 354(15):7028–7052

    Article  MATH  Google Scholar 

  30. Wang L, Shen Y, Zhang G (2016) Synchronization of a class of switched neural networks with time-varying delays via nonlinear feedback control. IEEE Trans Cybern 46(10):2300–2310

    Article  Google Scholar 

  31. Sader M, Abdurahman A, Jiang H (2018) General decay synchronization of delayed BAM neural networks via nonlinear feedback control. Appl Math Comput 337:302–314

    MathSciNet  MATH  Google Scholar 

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Acknowledgements

This work was supported by the Natural Science Foundation of the Xinjiang (Grant No. 2017D01C083).

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Authors and Affiliations

  1. College of Mathematics and System Sciences, Xinjiang University, ürümqi, 830046, Xinjiang, People’s Republic of China

    Malika Sader, Abdujelil Abdurahman & Haijun Jiang

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  1. Malika Sader
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  2. Abdujelil Abdurahman
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  3. Haijun Jiang
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Correspondence to Abdujelil Abdurahman.

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Sader, M., Abdurahman, A. & Jiang, H. General Decay Lag Synchronization for Competitive Neural Networks with Constant Delays. Neural Process Lett 50, 445–457 (2019). https://doi.org/10.1007/s11063-019-09984-w

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  • DOI: https://doi.org/10.1007/s11063-019-09984-w

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