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Fixed-time synchronization of fractional-order complex-valued delayed neural networks with discontinuous activation functions

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Abstract

This article concentrates on the fixed-time synchronization (FXTS) of fractional-order complex-valued delayed neural networks with discontinuous activation functions. On the basis of the nonsmooth analysis, differential inclusion theory, Lyapunov stability theorem and complex function theory, some sufficient conditions are developed to guarantee the FXTS of such system by designing a novel fractional-order complex-valued controller. The fixed-time synchronization can make up the limitation of the previous finite-time synchronization results, that is, fixed-time synchronization time relies on the parameters of controller, which is independent of initial values. Additionally, the upper limit of synchronization time is estimated accurately. Furthermore, our results improve some finite-time synchronization and fixed-time synchronization ones. Finally, the effectiveness of theoretical results is demonstrated by some numerical simulations.

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References

  1. Sabatier JATMJ, Agrawal OP, Machado JAT (2007) Advances in fractional calculus, vol 4. Springer, Dordrecht

    Book  Google Scholar 

  2. Thanh NT, Niamsup P, Phat VN (2021) New results on finite-time stability of fractional-order neural networks with time-varying delay. Neural Comput Appl 33:17489–17496

    Article  Google Scholar 

  3. Liu S, Yu Y, Zhang S (2019) Robust synchronization of memristor-based fractional-order Hopfield neural networks with parameter uncertainties. Neural Comput Appl 31:3533–3542

    Article  Google Scholar 

  4. Wan L, Liu Z (2020) Multiple o (t-a) stability for fractional-order neural networks with time-varying delays. J Frankl Inst 357(17):12742–12766

    Article  MathSciNet  Google Scholar 

  5. Chen L, Liu C, Wu R, He Y, Chai Y (2016) Finite-time stability criteria for a class of fractional-order neural networks with delay. Neural Comput Appl 27:549–556

    Article  Google Scholar 

  6. Ding Z, Yang L, Ye Y, Li S, Huang Z (2023) Passivity and passification of fractional-order memristive neural networks with time delays. ISA trans 137:314–322

    Article  Google Scholar 

  7. Zhang H, Ding Z, Zeng Z (2020) Adaptive tracking synchronization for coupled reaction-diffusion neural networks with parameter mismatches. Neural Netw 124:146–157

    Article  Google Scholar 

  8. Aouiti C, Bessifi M (2021) Sliding mode control for finite-time and fixed-time synchronization of delayed complex-valued recurrent neural networks with discontinuous activation functions and nonidentical parameters. Eur J Control 59:109–122

    Article  MathSciNet  Google Scholar 

  9. Ding Z, Zhang H, Zeng Z, Yang L, Li S (2021) Global dissipativity and quasi-Mittag-Leffler synchronization of fractional-order discontinuous complex-valued neural networks. IEEE Trans Neural Netw Learn Syst 34(8):4139–4152

    Article  MathSciNet  Google Scholar 

  10. Zhang X, Niu P, Liu N, Li G (2019) Global synchronization in finite-time of fractional-order complex-valued delayed Hopfield neural networks. Int J Control Autom Syst 17(2):521–535

    Article  Google Scholar 

  11. Kang Q, Yang Q, Yang J, Gan Q, Li R (2022) Synchronization in finite-time of delayed fractional-order fully complex-valued dynamical networks via non-separation method. Entropy 24(10):1460

    Article  MathSciNet  Google Scholar 

  12. Arslan E, Narayanan G, Ali MS, Arik S, Saroha S (2020) Controller design for finite-time and fixed-time stabilization of fractional-order memristive complex-valued bam neural networks with uncertain parameters and time-varying delays. Neural Netw 130:60–74

    Article  Google Scholar 

  13. Dadras S, Momeni HR (2010) Control of a fractional-order economical system via sliding mode. Physica A 389(12):2434–2442

    Article  Google Scholar 

  14. Mitri F (2011) Vector wave analysis of an electromagnetic high-order Bessel vortex beam of fractional type \(\alpha\). Opt Lett 36(5):606–608

    Article  MathSciNet  Google Scholar 

  15. Wang G, Ding Z, Li S, Yang L, Jiao R (2022) Finite-time Mittag-Leffler synchronization of fractional-order complex-valued memristive neural networks with time delay. Chin Phys B 31(10):100201

    Article  Google Scholar 

  16. Liu X, Yu Y (2021) Synchronization analysis for discrete fractional-order complex-valued neural networks with time delays. Neural Comput Appl 33:10503–10514

    Article  Google Scholar 

  17. Hu T, He Z, Zhang X, Zhong S (2020) Finite-time stability for fractional-order complex-valued neural networks with time delay. Appl Math Comput 365:124715

    Article  MathSciNet  Google Scholar 

  18. Su L, Zhou L (2019) Exponential synchronization of memristor-based recurrent neural networks with multi-proportional delays. Neural Comput Appl 31:7907–7920

    Article  Google Scholar 

  19. Dong Y, Guo L, Hao J (2020) Robust exponential stabilization for uncertain neutral neural networks with interval time-varying delays by periodically intermittent control. Neural Comput Appl 32:2651–2664

    Article  Google Scholar 

  20. 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 

  21. Xu C, Tong D, Chen Q, Zhou W, Shi P (2019) Exponential stability of Markovian jumping systems via adaptive sliding mode control. IEEE Trans Syst Man Cybern 51(2):954–964

    Article  Google Scholar 

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

    Article  Google Scholar 

  23. Chen J, Zeng Z, Jiang P (2014) Global Mittag-Leffler stability and synchronization of memristor-based fractional-order neural networks. Neural Netw 51:1–8

    Article  Google Scholar 

  24. Yang S, Hu C, Yu J, Jiang H (2021) Projective synchronization in finite-time for fully quaternion-valued memristive networks with fractional-order. Chaos Solitons Fract 147:110911

    Article  MathSciNet  Google Scholar 

  25. Zhang L, Yang Y, Wang F, Sui X (2018) Lag synchronization for fractionalorder memristive neural networks with time delay via switching jumps mismatch. J Frankl Inst 355(3):1217–1240

    Article  Google Scholar 

  26. Wang G, Ding Z, Li S, Yang L, Jiao R (2022) Finite-time lag projective synchronization of nonidentical fractional delayed memristive neural networks. J Franklin Inst 359(18):10653–10675

    Article  MathSciNet  Google Scholar 

  27. Aouiti C, Bessifi M, Li X (2020) Finite-time and fixed-time synchronization of complex-valued recurrent neural networks with discontinuous activations and time-varying delays. Circuits Syst Signal Process 39:5406–5428

    Article  Google Scholar 

  28. Tong D, Ma B, Chen Q, Wei Y, Shi P (2023) Finite-time synchronization and energy consumption prediction for multilayer fractional-order networks. IEEE Trans Circuits Syst II Express Br 70(6):2176–2180

    Google Scholar 

  29. Wang L, Zhang CK (2022) Exponential synchronization of memristor-based competitive neural networks with reaction-diffusions and infinite distributed delays. IEEE Trans Neural Netw Learn Syst 35(1):745–758

    Article  MathSciNet  Google Scholar 

  30. Wang L, He H, Zeng Z (2019) Global synchronization of fuzzy memristive neural networks with discrete and distributed delays. IEEE Trans Fuzzy Syst 28(9):2022–2034

    Article  Google Scholar 

  31. Yang Z, Zhang Z (2022) Global asymptotic synchronisation of fuzzy inertial neural networks with time-varying delays by applying maximum-value approach. Int J Syst Sci 53(11):2281–2300

    Article  MathSciNet  Google Scholar 

  32. Zheng M, Li L, Peng H, Xiao J, Yang Y, Zhang Y, Zhao H (2018) Fixed-time synchronization of memristor-based fuzzy cellular neural network with time-varying delay. J Frankl Inst 355(14):6780–6809

    Article  MathSciNet  Google Scholar 

  33. Xiao J, Cheng J, Shi K, Zhang R (2021) A general approach to fixed-time synchronization problem for fractional-order multidimension-valued fuzzy neural networks based on memristor. IEEE Trans Fuzzy Syst 30(4):968–977

    Article  Google Scholar 

  34. Ren H, Shi P, Deng F, Peng Y (2020) Fixed-time synchronization of delayed complex dynamical systems with stochastic perturbation via impulsive pinning control. J Frankl Inst 357(17):12308–12325

    Article  MathSciNet  Google Scholar 

  35. Yang G, Tong D, Chen Q, Zhou W (2022) Fixed-time synchronization and energy consumption for kuramoto-oscillator networks with multilayer distributed control. IEEE Trans Circuits Syst II Express Br 70(4):1555–1559

    Google Scholar 

  36. Hu X, Wang L, Zhang CK, Wan X, He Y (2023) Fixed-time stabilization of discontinuous spatiotemporal neural networks with time-varying coefficients via aperiodically switching control. Sci China Inf Sci 66(5):1–14

    Article  MathSciNet  Google Scholar 

  37. Peng X, Wu H, Song K, Shi J (2017) Global synchronization in finite time for fractional-order neural networks with discontinuous activations and time delays. Neural Netw 94:46–54

    Article  Google Scholar 

  38. Boonsatit N, Rajendran S, Lim CP, Jirawattanapanit A, Mohandas P (2022) New adaptive finite-time cluster synchronization of neutral-type complex-valued coupled neural networks with mixed time delays. Fractal Fract 6(9):515

    Article  Google Scholar 

  39. Xiao J, Wu L, Wu A, Zeng Z, Zhang Z (2022) Novel controller design for finite-time synchronization of fractional-order memristive neural networks. Neurocomputing 512:494–502

    Article  Google Scholar 

  40. Yang Z, Zhang Z, Wang X (2022) New finite-time synchronization conditions of delayed multinonidentical coupled complex dynamical networks. Math Biosci Eng 20(2):3047–3069

    Article  MathSciNet  Google Scholar 

  41. Yang Z, Zhang Z (2022) Finite-time synchronization analysis for bam neural networks with time-varying delays by applying the maximum-value approach with new inequalities. Mathematics 10(5):835

    Article  Google Scholar 

  42. Liao H, Yang Z, Zhang Z, Zhou Y (2023) Finite-time synchronization for delayed inertial neural networks by the approach of the same structural functions. Neural Process Lett 55(4):4973–4988

    Article  Google Scholar 

  43. Zheng B, Hu C, Yu J, Jiang H (2020) Finite-time synchronization of fully complex-valued neural networks with fractional-order. Neurocomputing 373:70–80

    Article  Google Scholar 

  44. Wang L, Zeng Z, Hu J, Wang X (2017) Controller design for global fixed-time synchronization of delayed neural networks with discontinuous activations. Neural Netw 87:122–131

    Article  Google Scholar 

  45. Yang S, Yu J, Hu C, Jiang H (2018) Quasi-projective synchronization of fractional-order complex-valued recurrent neural networks. Neural Netw 104:104–113

    Article  Google Scholar 

  46. Sun Y, Liu Y (2020) Adaptive synchronization of fractional-order chaotic neural networks with unknown parameters and time-varying delays. Int J Innov Comput Inf Control 16(2):649–661

    Google Scholar 

  47. Filippov AF (2013) Differential equations with discontinuous righthand sides: control systems (vol 18). Springer

    Google Scholar 

  48. Liü H, He W, Han QL, Peng C (2018) Fixed-time synchronization for coupled delayed neural networks with discontinuous or continuous activations. Neurocomputing 314:143–153

    Article  Google Scholar 

  49. Aubin J, Cellina A (2012) Differential inclusions: set-valued maps and viability theory, vol 264. Springer

    Google Scholar 

  50. Li H, Hu C, Cao J, Jiang H, Alsaedi A (2019) Quasi-projective and complete synchronization of fractional-order complex-valued neural networks with time delays. Neural Netw 118:102–109

    Article  Google Scholar 

  51. Wang S, Zhang Z, Lin C, Chen J (2021) Fixed-time synchronization for complex-valued BAM neural networks with time-varying delays via pinning control and adaptive pinning control. Chaos Solitons Fract 153:111583

    Article  MathSciNet  Google Scholar 

  52. Zhang Z, Guo R, Liu X, Zhong M, Lin C, Chen B (2021) Fixed-time synchronization for complex-valued BAM neural networks with time delays. Asian J Control 23(1):298–314

    Article  MathSciNet  Google Scholar 

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Acknowledgements

The work was supported by the Natural Science Foundation of China under Grants 62176189 and 62106181, and the Scientific Research Fund of Wuhan Institute of Technology under Grant Nos. K201908 and K202017.

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Authors and Affiliations

  1. School of Electrical and Information Engineering, Wuhan Institute of Technology, Wuhan, 430205, China

    Zhixia Ding, Jianhao Wang, Sai Li, Le Yang & Liheng Wang

  2. Hubei Key Laboratory of Optical Information and Pattern Recognition, Wuhan, 430205, China

    Zhixia Ding, Jianhao Wang, Sai Li, Le Yang & Liheng Wang

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  1. Zhixia Ding
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  2. Jianhao Wang
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  3. Sai Li
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  4. Le Yang
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Correspondence to Sai Li.

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Ding, Z., Wang, J., Li, S. et al. Fixed-time synchronization of fractional-order complex-valued delayed neural networks with discontinuous activation functions. Neural Comput & Applic (2024). https://doi.org/10.1007/s00521-024-09904-7

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  • DOI: https://doi.org/10.1007/s00521-024-09904-7

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