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Finite-time and fixed-time function projective synchronization of competitive neural networks with noise perturbation

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Abstract

In this paper, finite-time and fixed-time function projective synchronization of competitive neural networks with time-varying delays and noise perturbation is studied. Firstly, different from the existing papers, a more flexible Lyapunov function is constructed based on p-norm and two hybrid controllers are designed in this paper. Secondly, based on the finite-time and fixed-time stability theory and stochastic analysis theory, some new and useful finite-time and fixed-time function projective synchronization criteria are obtained. Furthermore, the settling time is derived with the help of some lemmas and mathematical inequalities under the appropriate control scheme. Finally, illustrative examples are given to show the feasibility of the proposed method.

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References

  1. Cohen MA, Grossberg S (1983) Absolute stability of global pattern formation and parallel memory storage by competitive neural networks. IEEE Trans Syst Man Cybern 5:815–826. https://doi.org/10.1109/TSMC.1983.6313075

    Article  MathSciNet  Google Scholar 

  2. Meyer-Bae A, Ohl F, Scheich H (1996) Singular perturbation analysis of competitive neural networks with different time scales. Neural Comput 8(8):1731–1742. https://doi.org/10.1162/neco.1996.8.8.1731

    Article  Google Scholar 

  3. Mead CA, Mahowald MA (1988) A silicon model of early visual processing. Neural Netw 1(1):91–97. https://doi.org/10.1016/0893-6080(88)90024-X

    Article  Google Scholar 

  4. Azad HB, Mekhilef S, Ganapathy VG (2014) Long-term wind speed forecasting and general pattern recognition using neural networks. IEEE Trans Sustain Energy 5(2):546–553. https://doi.org/10.1109/TSTE.2014.2300150

    Article  Google Scholar 

  5. Tank DW, Hopfield JJ (1987) Neural computation by concentrating information in time. Proc Natl Acad Sci 84(7):1896–1900. https://doi.org/10.1073/pnas.84.7.1896

    Article  MathSciNet  Google Scholar 

  6. Madaeni SS, Shiri M, Kurdian AR (2015) Modeling, optimization, and control of reverse osmosis water treatment in Kazeroon power plant using neural network. Chem Eng Commun 202(1):6–14. https://doi.org/10.1080/00986445.2013.828606

    Article  Google Scholar 

  7. Arbi A, Cao J, Alsaedi A (2018) Improved synchronization analysis of competitive neural networks with time-varying delays. Nonlinear Anal Model Control 23(1):82–107. https://doi.org/10.15388/NA.2018.1.7

    Article  MathSciNet  Google Scholar 

  8. Lou X, Cui B (2007) Synchronization of competitive neural networks with different time scales. Phys A Stat Mech Appl 380:563–576. https://doi.org/10.1016/j.physa.2007.02.088

    Article  Google Scholar 

  9. Pratap A, Raja R, Agarwal RP et al (2019) Stability analysis and robust synchronization of fractional order competitive neural networks with different time scales and impulsive perturbations. Int J Adapt Control Signal Process 33(11):1635–1660. https://doi.org/10.1002/acs.3056

    Article  MathSciNet  Google Scholar 

  10. Shi Y, Zhu P (2014) Synchronization of memristive competitive neural networks with different time scales. Neural Comput Appl 25(5):1163–1168. https://doi.org/10.1007/s00521-014-1598-9

    Article  Google Scholar 

  11. Wu Y, Wang Y, Liu X et al (2021) Fixed-time synchronization of competitive neural networks with multiple time-scale. IEEE Trans Neural Netw Learn Syst 33(8):4133–4138. https://doi.org/10.1109/TNNLS.2021.3052868

    Article  MathSciNet  Google Scholar 

  12. Tan Y, Jing K (2016) Existence and global exponential stability of almost periodic solution for delayed competitive neural networks with discontinuous activations. Math Methods Appl Sci 39(11):2821–2839. https://doi.org/10.1002/mma.3732

    Article  MathSciNet  Google Scholar 

  13. Liu X, Yang C, Zhou L (2018) Global asymptotic stability analysis of two-time-scale competitive neural networks with time-varying delays. Neurocomputing 273:357–366. https://doi.org/10.1016/j.neucom.2017.07.047

    Article  Google Scholar 

  14. Yang W, Wang YW, Morǎrescu IC et al (2021) Fixed-time synchronization of competitive neural networks with multiple time scales. IEEE Trans Neural Netw Learn Syst 33(8):4133–4138. https://doi.org/10.1109/TNNLS.2021.3052868

    Article  MathSciNet  Google Scholar 

  15. Mainieri R, Rehacek J (1999) Projective synchronization in three-dimensional chaotic systems. Phys Rev Lett 82(15):3042. https://doi.org/10.1103/PhysRevLett.82.3042

    Article  Google Scholar 

  16. Aadhithiyan S, Raja R, Zhu Q et al (2021) Modified projective synchronization of distributive fractional order complex dynamic networks with model uncertainty via adaptive control. Chaos Solitons Fractals 147:110853. https://doi.org/10.1016/j.chaos.2021.110853

    Article  MathSciNet  Google Scholar 

  17. Du H, Shi P, Lü N (2013) Function projective synchronization in complex dynamical networks with time delay via hybrid feedback control. Nonlinear Anal Real World Appl 14(2):1182–1190. https://doi.org/10.1016/j.nonrwa.2012.09.009

    Article  MathSciNet  Google Scholar 

  18. Abdurahman A, Jiang H, Rahman K (2015) Function projective synchronization of memristor-based Cohen Grossberg neural networks with time-varying delays. Cogn Neurodyn 9(6):603–613. https://doi.org/10.1007/s11571-015-9352-2

    Article  Google Scholar 

  19. Al-Azzawi SF, Al-Talib ZS (2022) Generalized function projective synchronization via nonlinear controller strategy. J Interdiscip Math. https://doi.org/10.1080/09720502.2021.2008625

    Article  Google Scholar 

  20. Wang L, Zhang C (2022) Exponential synchronization of memristor-based competitive neural networks with reaction-diffusions and infinite distributed delays. IEEE Trans Neural Netw Learn Syst. https://doi.org/10.1109/TNNLS.2022.3176887

    Article  Google Scholar 

  21. Wang L, He H, Zeng Z (2020) Global synchronization of fuzzy memristive neural networks with discrete and distributed delays. IEEE Trans Fuzzy Syst 28(9):2022–2034. https://doi.org/10.1109/TFUZZ.2019.2930032

    Article  Google Scholar 

  22. Fan Y, Wang L, Xing K et al (2016) Projective synchronization adaptive control for different chaotic neural networks with mixed time delays. Optik 127(5):2551–2557. https://doi.org/10.1016/j.ijleo.2015.11.227

    Article  Google Scholar 

  23. Li M, Yang X, Song Q et al (2022) Robust asymptotic stability and projective synchronization of time-varying delayed fractional neural networks under parametric uncertainty. Neural Process Lett 54(4):4661–4680. https://doi.org/10.1007/s11063-022-10825-6

    Article  Google Scholar 

  24. Duan L, Zhang M, Zhao J (2019) Finite-time synchronization of delayed competitive neural networks with different time scales. J Inf Optim Sci 40(4):813–837. https://doi.org/10.1080/02522667.2018.1453670

    Article  MathSciNet  Google Scholar 

  25. Zou Y, Yang X, Tang R et al (2020) Finite-time quantized synchronization of coupled discontinuous competitive neural networks with proportional delay and impulsive effects. J Frankl Inst 357(16):11136–11152. https://doi.org/10.1016/j.jfranklin.2019.05.017

    Article  MathSciNet  Google Scholar 

  26. Polyakov A (2011) Nonlinear feedback design for fixed-time stabilization of linear control systems. IEEE Trans Autom Control 57(8):2106–2110. https://doi.org/10.1109/TAC.2011.2179869

    Article  MathSciNet  Google Scholar 

  27. Zheng C, Hu C, Yu J et al (2022) Fixed-time synchronization of discontinuous competitive neural networks with time-varying delays. Neural Netw 153:192–203. https://doi.org/10.1016/j.neunet.2022.06.002

    Article  Google Scholar 

  28. Zhao Y, Ren S, Kurths J (2021) Finite-time and fixed-time synchronization for a class of memristor-based competitive neural networks with different time scales. Chaos Solitons Fractals 148:111033. https://doi.org/10.1016/j.chaos.2021.111033

    Article  MathSciNet  Google Scholar 

  29. Khalil HK, Grizzle JW (2002) Nonlinear systems. Prentice Hall, Upper Saddle River

    Google Scholar 

  30. Li L, Jian J (2014) Finite-time synchronization of chaotic complex networks with stochastic disturbance. Entropy 17(1):39–51. https://doi.org/10.3390/e17010039/

    Article  MathSciNet  Google Scholar 

  31. Ren H, Peng Z, Gu Y (2020) Fixed-time synchronization of stochastic memristor-based neural networks with adaptive control. Neural Netw 130:165–175. https://doi.org/10.1016/j.neunet.2020.07.002

    Article  Google Scholar 

  32. Jia T, Chen X, Zhao F et al (2023) Adaptive fixed-time synchronization of stochastic memristor-based neural networks with discontinuous activations and mixed delays. J Frankl Inst 360(4):3364–3388. https://doi.org/10.1016/j.jfranklin.2022.11.006

    Article  MathSciNet  Google Scholar 

  33. Wang P, Li X, Lu J et al (2023) Fixed-time synchronization of stochastic complex-valued fuzzy neural networks with memristor and proportional delays. Neural Process Lett. https://doi.org/10.1007/s11063-023-11320-2

    Article  Google Scholar 

  34. Qin X, Wang C, Li L et al (2019) Finite-time projective synchronization of memristor-based neural networks with leakage and time-varying delays. Phys A 531:121788. https://doi.org/10.1016/j.physa.2019.121788

    Article  MathSciNet  Google Scholar 

  35. Feng L, Hu C, Yu J et al (2021) Fixed-time synchronization of coupled memristive complex-valued neural networks. Chaos Solitons Fractals 148:110993. https://doi.org/10.1016/j.chaos.2021.110993

    Article  MathSciNet  Google Scholar 

  36. Li Q, Liu S (2017) Dual-stage adaptive finite-time modified function projective multi-lag combined synchronization for multiple uncertain chaotic systems. Open Math 15(1):1035–1047. https://doi.org/10.1515/math-2017-0087

    Article  MathSciNet  Google Scholar 

  37. Zhang M, Han M (2016) Finite-time projective synchronization control of uncertain complex networks with brushless DC motor and Rikitake system. In: Eighth international conference on advanced computational intelligence. IEEE, pp 100–107

  38. Li Q, Liu S (2018) Two-stage adaptive finite-time modified function projective lag synchronization of chaotic systems. In: Chinese control and decision conference. IEEE, pp 649–654

  39. Zhang M, Han M (2015) Finite-time signal lag-projective synchronous transmission between uncertain complex networks with NH3 and CO2 lasers. In: Chinese automation congress. IEEE, pp 835–840

  40. Chen W, Jiao LC (2010) Finite-time stability theorem of stochastic nonlinear systems. Automatica 46(12):2105–2108. https://doi.org/10.1016/j.automatica.2010.08.009

    Article  MathSciNet  Google Scholar 

  41. Zhang Z, Wang Z, Chen J, et al (2022) (Anti)-synchronization for CVINNs with time-varying delays. In: Shen D (ed) Complex-valued neural networks systems with time delay. Springer, Singapore 161–179

  42. Liu Y, Zhang G, Hu J (2022) Fixed-time anti-synchronization and preassigned-time synchronization of discontinuous fuzzy inertial neural networks with bounded distributed time-varying delays. Neural Process Lett. https://doi.org/10.1007/s11063-022-11011-4

    Article  Google Scholar 

  43. Yu J, Yu S, Li J et al (2019) Fixed-time stability theorem of stochastic nonlinear systems. Int J Control 92(9):2194–2200. https://doi.org/10.1080/00207179.2018.1430900

    Article  MathSciNet  Google Scholar 

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Acknowledgements

The authors are grateful for the support of the National Natural Science Foundation of China [Grant 61304162].

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Authors and Affiliations

  1. Three Gorges Mathematical Research Center, China Three Gorges University, Yichang, 443002, People’s Republic of China

    Caiqing Hao, Baoxian Wang & Dandan Tang

  2. College of Science, China Three Gorges University, Yichang, 443002, People’s Republic of China

    Caiqing Hao, Baoxian Wang & Dandan Tang

Authors
  1. Caiqing Hao
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  2. Baoxian Wang
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Contributions

Caiqing Hao was involved in writing—original draft, formal analysis, investigation, and software. Baoxian Wang contributed to the conceptualization, methodology, writing—review and editing, supervision, project administration, and funding acquisition. Dandan Tang contributed to software, visualization, and validation.

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Correspondence to Baoxian Wang.

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Hao, C., Wang, B. & Tang, D. Finite-time and fixed-time function projective synchronization of competitive neural networks with noise perturbation. Neural Comput & Applic 36, 16527–16543 (2024). https://doi.org/10.1007/s00521-024-09885-7

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  • DOI: https://doi.org/10.1007/s00521-024-09885-7

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