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Fixed-Time Lag Synchronization Analysis for Delayed Memristor-Based Neural Networks

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Abstract

In this paper, the fixed-time lag synchronization for a general class of memristor-based neural networks (MNNs) with time delays is considered. Under the extended Filippov-framework theory, some sufficient criteria for fixed-time lag synchronization of delayed MNNs are derived based on the Lyapunov function. Besides, two types of controllers are given to ensure the fixed-time lag synchronization of the corresponding system, while the settling time of synchronization are also estimated. Finally, a numerical example is given to demonstrate the effectiveness of the developed method and the theoretical results.

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References

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

    Google Scholar 

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

    Google Scholar 

  3. Merrikh-Bayat F, Shouraki S (2011) Memristor-based circuits for performing basic arithmetic operations. Procedia Comput Sci 3:128–132

    Google Scholar 

  4. Pershin Y, Ventra M (2010) Experimental demonstration of associative memory with memristive neural networks. Neural Netw 23:881–886

    Google Scholar 

  5. Snider G (2007) Self-organized computation with unreliable, memristive nanodevices. Nanotechnology 18:365202

    Google Scholar 

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

    Google Scholar 

  7. Bao H, Park J, Cao J (2019) Non-fragile state estimation for fractional-order delayed memristive BAM neural networks. Neural Netw 119:190–199

    MATH  Google Scholar 

  8. Adhikari S, Yang C, Kim H, Chua L (2012) Memristor bridge synapse-based neural network and its learning. IEEE Trans Neural Netw Learn Syst 23:1426–1435

    Google Scholar 

  9. Bao H, Cao J, Kurths J, Alsaedi A, Ahmad B (2018) \(H_{\infty }\) state estimation of stochastic memristor-based neural networks with time-varying delays. Neural Netw 99:79–91

    MATH  Google Scholar 

  10. Lu H, Yu D, Fitch A, Sreeram V, Chen H (2011) Controlling chaos in a memristor based circuit using a Twin–Tnotch filter. IEEE Trans Circuits Syst I Regul Pap 58:1337–1344

    MathSciNet  Google Scholar 

  11. Bao H, Cao J, Kurths J (2018) State estimation of fractional-order delayed memristive neural networks. Nonlinear Dyn 94:1215–1225

    Google Scholar 

  12. Li L, Ho D, Cao J, Lu J (2016) Pinning cluster synchronization in an array of coupled neural networks under event-based mechanism. Neural Netw 76:1–12

    MATH  Google Scholar 

  13. Huang C, Wang W, Cao J, Lu J (2018) Synchronization-based passivity of partially coupled neural networks with event-triggered communication. Neurocomputing 319:134–143

    Google Scholar 

  14. Li Y (2017) Impulsive synchronization of stochastic neural networks via controlling partial states. Neural Process Lett 46:59–69

    Google Scholar 

  15. Huang C, Lu J, Ho D, Zhai G, Cao J (2020) Stabilization of probabilistic boolean networks via pinning control strategy. Inf Sci 510:205–217

    MathSciNet  Google Scholar 

  16. Li L, Ho D, Lu J (2017) Event-based network consensus with communication delays. Nonlinear Dyn 87:1847–1858

    MATH  Google Scholar 

  17. Yang J, Lu J, Lou J, Lou J, Liu Y (2020) Synchronization of drive-response boolean control networks with impulsive disturbances. Appl Math Comput 364:124679

    MathSciNet  MATH  Google Scholar 

  18. Li Y, Lou J, Wang Z, Alsaadi F (2018) Synchronization of dynamical networks with nonlinearly coupling function under hybrid pinning impulsive controllers. J Frankl Inst 355:6520–6530

    MathSciNet  MATH  Google Scholar 

  19. Yang T, Chua L (1997) Impulsive stabilization for control and synchronization of chaotic systems: theory and application to secure communication. IEEE Trans Circuits Syst I Fundam Theory Appl 44:976–988

    MathSciNet  Google Scholar 

  20. Chen G, Dong X (1998) From chaos to order: methodologies, perspectives and applications. World Scientific, Singapore

    MATH  Google Scholar 

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

    MathSciNet  Google Scholar 

  22. Wang X, She K, Zhong S, Cheng J (2017) Exponential synchronization of memristor-based neural networks with time-varying delay and stochastic perturbation. Neurocomputing 242:131–139

    Google Scholar 

  23. Shi Y, Cao J, Chen G (2017) Exponential stability of complex-valued memristor-based neural networks with time-varying delays. Appl Math Comput 313:222–234

    MathSciNet  MATH  Google Scholar 

  24. Bao H, Cao J (2015) Projective synchronization of fractional-order memristor-based neural networks. Neural Netw 63:1–9

    MATH  Google Scholar 

  25. Abdurahman A, Jiang H, Teng Z (2016) Exponential lag synchronization for memristor-based neural networks with mixed-time delays via hybird switching control. J Frankl Inst 353:2859–2880

    MATH  Google Scholar 

  26. Abdurahman A, Jiang H, Teng Z (2015) Finite-time synchronization for memristor-based neural networks with time-varying delays. Neural Netw 69:20–28

    MATH  Google Scholar 

  27. Polyakov A (2012) Nonlinear feedback design for fixed-time stabilization of linear control systems. IEEE Trans Autom Control 57:2106–2110

    MathSciNet  MATH  Google Scholar 

  28. Jiang B, Hu Q, Friswell M (2016) Fixed-time attitute control for rigid space-craft with actuator saturation and faults. IEEE Trans Control Syst Technol 24:1892–1898

    Google Scholar 

  29. Ni J, Liu L, Liu C, Hu X, Li S (2017) Fast fixed-time nonsingular terminal sliding mode control and its application to chaos suppression in power system. IEEE Trans Circuits Syst II Express Briefs 64:151–155

    Google Scholar 

  30. Hu C, Yu J, Chen Z, Jiang H, Huang T (2017) Fixed-time stability of dynamical systems and fixed-time synchronization of coupled discontinuous neural networks. Neural Netw 89:74–83

    MATH  Google Scholar 

  31. Cao J, Li R (2017) Fixed-time synchronization of delayed memristor-based recurrent neural networks. Sci China Inf Sci 60:032201

    Google Scholar 

  32. Wan Y, Cao J, Wen G, Yu W (2016) Robust fixed-time synchronization of delayed Cohen–Grossberg neural networks. Neural Netw 73:86–94

    MATH  Google Scholar 

  33. Ding X, Cao J, Alsaedi A, Alsaadi F, Hayat T (2017) Robust fixed-time synchronization for uncertain complex-valued neural networks with discontinuous activation functions. Neural Netw 90:42–55

    MATH  Google Scholar 

  34. Chen C, Li L, Peng H, Yang Y (2017) Fixed-time synchronization of memristor-based BAM neural networks with time-varying discere-delay. Neural Netw 96:47–54

    MATH  Google Scholar 

  35. Li H, Li C, Huang T, Zhang W (2018) Fixed-time stabilization of impulsive Cohen–Grossberg BAM neural networks. Neural Netw 98:203–211

    MATH  Google Scholar 

  36. Xu Y, Meng D, Xie C, You G, Zhou W (2018) A class of fast fixed-time synchronization control for the delayed neural network. J Frankl Inst 355:164–176

    MathSciNet  MATH  Google Scholar 

  37. Li J, Jiang H, Hu C, Yu Z (2018) Multiple types of synchronization analysis for discontinuous Cohen–Grossberg neural networks with time-varying delays. Neural Netw 99:101–113

    MATH  Google Scholar 

  38. Liu Q, Zhang S (2012) Adaptive lag synchronization of chaotic Cohen–Grossberg neural networks with discrete delays. Chaos Interdiscip J Nonlinear Sci 22:033123

    MathSciNet  MATH  Google Scholar 

  39. Li N, Cao J (2015) Lag synchronization of memristor-based coupled neural networks via \(\omega \)-measure. IEEE Trans Neural Netw Learn Syst 27:686–697

    MathSciNet  Google Scholar 

  40. Wang L, Yuan Z, Chen X, Zhou Z (2011) Lag synchronization of chaotic systems with parameter mismatches. Commun Nonlinear Sci Numer Simul 16:987–992

    MathSciNet  MATH  Google Scholar 

  41. Wang W, Li L, Peng H, Xiao J, Yang Y (2014) Synchronization control of memristor-based recurrent neural networks with perturbations. Neural Netw 53:8–14

    MATH  Google Scholar 

  42. Filippov A (1988) Differential equations with discontinuous righthand side. Mathematics and its applications. Kluwer, Boston

    Google Scholar 

  43. Clarke F, Ledyaev Y, Stern R, Wolenski P (1998) Nonsmooth analysis and control theory. Graduate texts in mathematics. Springer, New York

    MATH  Google Scholar 

  44. Clarke F (1990) Optimization and nonsmooth analysis. SIAM, Philadelphia

    MATH  Google Scholar 

  45. Hardy G, Littlewood J, Polya G (1952) Inequalities. Cambridge University Press, Cambridge

    MATH  Google Scholar 

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Authors and Affiliations

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

    Xiahedan Haliding, Haijun Jiang, Abdujelil Abdurahman & Cheng Hu

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  1. Xiahedan Haliding
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  2. Haijun Jiang
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  3. Abdujelil Abdurahman
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  4. Cheng Hu
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Correspondence to Haijun Jiang.

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This was supported in part by the National Natural Science Foundation of People’s Republic of China (Grant Nos. U1703262, 61563048, 61703358).

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Haliding, X., Jiang, H., Abdurahman, A. et al. Fixed-Time Lag Synchronization Analysis for Delayed Memristor-Based Neural Networks. Neural Process Lett 52, 485–509 (2020). https://doi.org/10.1007/s11063-020-10249-0

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