Computers and Concrete

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Exponential stability of stochastic static neutral neural networks with varying delays

  • Sun, Xiaoqi (School of Mathematics and Statistics, Qingdao University)
  • Received : 2022.03.26
  • Accepted : 2022.06.16
  • Published : 2022.10.25
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Abstract

This paper is concerned with exponential stability in mean square for stochastic static neutral neural networks with varying delays. By using Lyapunov functional method and with the help of stochastic analysis technique, the sufficient conditions to guarantee the exponential stability in mean square for the neural networks are obtained and some results of related literature are extended.

Keywords

Acknowledgement

Natural Science Foundation of Shandong Province ZR2019PA007.

References

  1. Al-Furjan, M., Moghadam, S.A., Dehini, R., Shan, L., Habibi, M. and Safarpour, H. (2020), "Vibration control of a smart shell reinforced by graphene nanoplatelets under external load: Semi-numerical and finite element modeling", Thin Wall. Struct., 159, 107242. https://doi.org/10.1016/j.tws.2020.107242.
  2. Bao, H. and Cao, J. (2011), "Stochastic global exponential stability for neutral-type impulsive neural networks with mixed time-delays and Markovian jumping parameters", Commun. Nonlin. Sci. Numer. Simul., 16(9), 3786-3791. https://doi.org/10.1016/j.cnsns.2010.12.027.
  3. Cao, B., Zhao, J., Liu, X., Arabas, J., Tanveer, M., Singh, A.K. and Lv, Z. (2022), "Multiobjective evolution of the explainable fuzzy rough neural network with gene expression programming", IEEE Trans. Fuzzy Syst., 30(10), 4190-4200. https://doi.org/10.1109/tfuzz.2022.3141761.
  4. Chen, G., Li, D., Shi, L., van Gaans, O. and Verduyn Lunel, S. (2018), "Stability results for stochastic delayed recurrent neural networks with discrete and distributed delays", J. Differ. Eq., 264(6), 3864-3898. https://doi.org/10.1016/j.jde.2017.11.032.
  5. Chen, H., Miao, Y., Chen, Y., Fang, L., Zeng, L. and Shi, J. (2021), "Intelligent model-based integrity assessment of nonstationary mechanical system", J. Web Eng., 20(2), 253-280. https://doi.org/10.13052/jwe1540-9589.2022.
  6. Cheshmeh, E., Karbon, M., Eyvazian, A., Jung, D.W., Habibi, M. and Safarpour, M. (2020), "Buckling and vibration analysis of FG-CNTRC plate subjected to thermo-mechanical load based on higher order shear deformation theory", Mech. Bas. Des. Struct. Mach., 50(4), 1137-1160. https://doi.org/10.1080/15397734.2020.1744005.
  7. Cui, H., Guo, J., Feng, J. and Wang, T. (2015), "Global μ-stability of impulsive reaction-diffusion neural networks with unbounded time-varying delays and bounded continuously distributed delays", Neurocomput., 157, 1-10. https://doi.org/10.1016/j.neucom.2015.01.044.
  8. Dai, Z., Jiang, Z., Zhang, L. and Habibi, M. (2021), "Frequency characteristics and sensitivity analysis of a size-dependent laminated nanoshell", Adv. Nano Res., 10(2), 175. https://doi.org/10.12989/anr.2021.10.2.175.
  9. Gong, X., Wang, L., Mou, Y., Wang, H., Wei, X., Zheng, W. and Yin, L. (2022), "Improved four-channel PBTDPA control strategy using force feedback bilateral teleoperation system", Int. J. Control, Auto. Syst., 20(3), 1002-1017. https://doi.org/10.1007/s12555-021-0096-y.
  10. Guo, J., Baharvand, A., Tazeddinova, D., Habibi, M., Safarpour, H., Roco-Videla, A. and Selmi, A. (2021), "An intelligent computer method for vibration responses of the spinning multi-layer symmetric nanosystem using multi-physics modeling", Eng. Comput., 1-22. https://doi.org/10.1007/s00366-021-01433-4.
  11. Hashemi, H.R., Alizadeh, A.A., Oyarhossein, M.A., Shavalipour, A., Makkiabadi, M. and Habibi, M. (2019), "Influence of imperfection on amplitude and resonance frequency of a reinforcement compositionally graded nanostructure", Wave. Random Complex Media, 1-27. https://doi.org/10.1080/17455030.2019.1662968.
  12. Hou, F., Wu, S., Moradi, Z. and Shafiei, N. (2021), "The computational modeling for the static analysis of axially functionally graded micro-cylindrical imperfect beam applying the computer simulation", Eng. Comput., 1-19. https://doi.org/10.1007/s00366-021-01456-x.
  13. Huang, X., Zhu, Y., Vafaei, P., Moradi, Z. and Davoudi, M. (2021), "An iterative simulation algorithm for large oscillation of the applicable 2D-electrical system on a complex nonlinear substrate", Eng. Comput., 38(4), 3137-3149. https://doi.org/10.1007/s00366-021-01320-y.
  14. Jiang, Y. and Li, X. (2022), "Broadband cancellation method in an adaptive co-site interference cancellation system", Int. J. Electron., 109(5), 854-874. https://doi.org/10.1080/00207217.2021.1941295.
  15. Jifu, N. (2012), "Global exponential stability of delayed Hopfield neural networks", 2012 International Conference on Computer Science and Information Processing (CSIP), August.
  16. Li, D., Yu, H., Tee, K.P., Wu, Y., Ge, S.S. and Lee, T.H. (2022a), "On time-synchronized stability and control", IEEE Trans. Syst. Man Cybernet.: Syst., 52(4), 2450-2463. https://doi.org/10.1109/TSMC.2021.3050183.
  17. Li, J., Xu, K., Chaudhuri, S., Yumer, E., Zhang, H. and Guibas, L. (2017), "GRASS: Generative recursive autoencoders for shape structures", Acta Electronica Malaysia, 36(4), Article 52. https://doi.org/10.1145/3072959.3073637.
  18. Li, P., Li, Y., Gao, R., Xu, C. and Shang, Y. (2022b), "New exploration on bifurcation in fractional-order genetic regulatory networks incorporating both type delays", Eur. Phys. J. Plus, 137(5), 598. https://doi.org/10.1140/epjp/s13360-022-02726-3.
  19. Li, X., Ding, D. and Sang, D. (2018), "Exponential stability of stochastic cellular neural networks with mixed delays", Commun. Stat.-Theor. Meth., 47(19), 4881-4894. https://doi.org/10.1080/03610926.2018.1459710.
  20. Liu, H., Wang, Z., Shen, B., Huang, T. and Alsaadi, F.E. (2018), "Stability analysis for discrete-time stochastic memristive neural networks with both leakage and probabilistic delays", Neur. Network., 102 1-9. https://doi.org/10.1016/j.neunet.2018.02.003.
  21. Liu, K. (2015), "Some views on recent randomized study of infinite dimensional functional differential equations", Scientia Sinica Mathematica, 45(5), 559-566. https://doi.org/10.1360/N012015-00055.
  22. Liu, Y., Wang, W., He, T., Moradi, Z. and Larco Benitez, M.A. (2021), "On the modelling of the vibration behaviors via discrete singular convolution method for a high-order sector annular system", Eng. Comput., 1-23. https://doi.org/10.1007/s00366-021-01454-z.
  23. Liu, Z., Su, S., Xi, D. and Habibi, M. (2020), "Vibrational responses of a MHC viscoelastic thick annular plate in thermal environment using GDQ method", Mech. Bas. Des. Struct. Mach., 50(8), 2688-2713. https://doi.org/10.1080/15397734.2020.1784201.
  24. Lori, E.S., Ebrahimi, F., Supeni, E.E.B., Habibi, M. and Safarpour, H. (2020), "The critical voltage of a GPL-reinforced composite microdisk covered with piezoelectric layer", Eng. Comput., 37(4), 3489-3508. https://doi.org/10.1007/s00366-020-01004-z.
  25. Ma, L., Liu, X. and Moradi, Z. (2022), "On the chaotic behavior of graphene-reinforced annular systems under harmonic excitation", Eng. Comput., 38(3), 2583-2607. https://doi.org/10.1007/s00366-020-01210-9.
  26. Ma, Z., Zheng, W., Chen, X. and Yin, L. (2021), "Joint embedding VQA model based on dynamic word vector", PeerJ. Comput. Sci., 7, e353. https://doi.org/10.7717/peerj-cs.353.
  27. Mao, X. (2007), Stochastic Differential Equations and Applications, Elsevier
  28. Meng, Z. and Xiang, Z. (2017), "Stability analysis of stochastic memristor-based recurrent neural networks with mixed time-varying delays", Neur. Comput. Appl., 28(7), 1787-1799. https://doi.org/10.1007/s00521-015-2146-y.
  29. Najaafi, N., Jamali, M., Habibi, M., Sadeghi, S., Jung, D.W. and Nabipour, N. (2020), "Dynamic instability responses of the substructure living biological cells in the cytoplasm environment using stress-strain size-dependent theory", J. Biomolec. Struct. Dyn., 39(7), 2543-2554. https://doi.org/10.1080/07391102.2020.1751297.
  30. Niu, Z., Zhang, B., Dai, B., Zhang, J., Shen, F., Hu, Y., Fan, Y. and Zhang, Y. (2022), "220 GHz multi circuit integrated front end based on solid-state circuits for high speed communication system", Chin. J. Electron., 31(3), 569-580. https://doi.org/10.1049/cje.2021.00.295.
  31. Rakkiyappan, R., Balasubramaniam, P. and Cao, J. (2010), "Global exponential stability results for neutral-type impulsive neural networks", Nonlin. Anal.: Real World Appl., 11(1), 122-130. https://doi.org/10.1016/j.nonrwa.2008.10.050.
  32. Rao, R. and Zhong, S. (2017), "Stability analysis of impulsive stochastic reaction-diffusion cellular neural network with distributed delay via fixed point theory", Complex., 2017, Article ID 6292597. https://doi.org/10.1155/2017/6292597.
  33. Sen, S.C., Kasim, S., Fudzee, M.F.M., Abdullah, R. and Atan, R. (2017), "Random walk from different perspective", Acta Electronica Malaysia, 1(2), 26-27. https://doi.org/10.26480/aem.02.2017.26.27.
  34. Shao, Y., Zhao, Y., Gao, J. and Habibi, M. (2021), "Energy absorption of the strengthened viscoelastic multi-curved composite panel under friction force", Arch. Civil Mech. Eng., 21(4), 1-29. https://doi.org/10.1007/s43452-021-00279-3.
  35. Shariati, A., Mohammad-Sedighi, H., Zur, K.K., Habibi, M. and Safa, M. (2020), "Stability and dynamics of viscoelastic moving rayleigh beams with an asymmetrical distribution of material parameters", Symmetry, 12(4), 586. https://doi.org/10.3390/sym12040586.
  36. Sun, G., Cong, Y., Wang, Q., Zhong, B. and Fu, Y. (2022), "Representative task self-selection for flexible clustered lifelong learning", IEEE Trans. Neur. Network. Learn. Syst., 33(4), 1467-1481. https://doi.org/10.1109/TNNLS.2020.3042500.
  37. Tan, J., Li, C. and Huang, T. (2015), "The stability of impulsive stochastic Cohen-Grossberg neural networks with mixed delays and reaction-diffusion terms", Cognit. Neurodyn., 9(2), 213-220. https://doi.org/10.1007/s11571-014-9316-y.
  38. Wang, J., Tian, J., Zhang, X., Yang, B., Liu, S., Yin, L. and Zheng, W. (2022), "Control of time delay force feedback teleoperation system with finite time convergence", Front. Neurorobot., 16, 877069-877069. https://doi.org/10.3389/fnbot.2022.877069.
  39. Wang, L. (2016), "Global well-posedness and stability of the mild solutions for a class of stochastic partial functional differential equations", Scientia Sinica Mathematica, 47(3), 371-382. https://doi.org/10.1360/012016-14.
  40. Wang, L., Zhang, R. and Wang, Y. (2009), "Global exponential stability of reaction-diffusion cellular neural networks with S-type distributed time delays", Nonlin. Anal: Real World Appl., 10(2), 1101-1113. https://doi.org/10.1016/j.nonrwa.2007.12.002.
  41. Wang, Z., Yu, S., Xiao, Z. and Habibi, M. (2020), "Frequency and buckling responses of a high-speed rotating fiber metal laminated cantilevered microdisk", Mech. Adv. Mater. Struct., 29(10), 1475-1488. https://doi.org/10.1080/15376494.2020.1824284.
  42. Wu, J. and Habibi, M. (2021), "Dynamic simulation of the ultra-fast-rotating sandwich cantilever disk via finite element and semi-numerical methods", Eng. Comput., 1-17. https://doi.org/10.1007/s00366-021-01396-6.
  43. Wu, M., Zhang, B., Zhou, Y. and Huang, K. (2022), "A double-fold 7×8 butler matrix-fed multibeam antenna with a boresight beam for 5G applications", IEEE Antenna. Wirel. Propag. Lett., 21(3), 516-520. https://doi.org/10.1109/lawp.2021.3136913.
  44. Xiong, Q.M., Chen, Z., Huang, J.T., Zhang, M., Song, H., Hou, X.F., Li, X.B. and Feng, Z.J. (2020), "Preparation, structure and mechanical properties of Sialon ceramics by transition metal-catalyzed nitriding reaction", Rare Metal., 39(5), 589-596. https://doi.org/10.1007/s12598-020-01385-6.
  45. Xu, D., Wang, X. and Yang, Z. (2013), "Further results on existence-uniqueness for stochastic functional differential equations", Science China Math., 56(6), 1169-1180. https://doi.org/10.1007/s11425-012-4553-1.
  46. Yao, H. and Yuan, F. (2018), "Exponential stability control for networked system with interval distribution time delays", Acta Informatica Malaysia, 2(1), 07-09. https://doi.org/10.26480/aim.01.2018.07.09
  47. Yu, X., Maalla, A. and Moradi, Z. (2022), "Electroelastic high-order computational continuum strategy for critical voltage and frequency of piezoelectric NEMS via modified multi-physical couple stress theory", Mech. Syst. Signal Pr., 165, 108373. https://doi.org/10.1016/j.ymssp.2021.108373.
  48. Zhang, J., Zhu, C., Zheng, L. and Xu, K. (2021), "ROSEFusion: Random optimization for online dense reconstruction under fast camera motion", ACM Trans. Graph., 40(4), 1-17. https://doi.org/10.1145/3450626.3459676.
  49. Zhang, W. and Wang, L. (2012), "Robust stochastic stability analysis for uncertain neutral-type delayed neural networks driven by wiener process", J. Appl. Math., 2012, Article ID 829594. https://doi.org/10.1155/2012/829594.
  50. Zhou, C., Zhao, Y., Zhang, J., Fang, Y. and Habibi, M. (2020), "Vibrational characteristics of multi-phase nanocomposite reinforced circular/annular system", Adv. Nano Res., 9(4), 295-307. https://doi.org/10.12989/anr.2020.9.4.295.
  51. Zhu, B., Zhong, Q., Chen, Y., Liao, S., Li, Z., Shi, K. and Sotelo, M.A. (2022), "A novel reconstruction method for temperature distribution measurement based on ultrasonic tomography", IEEE Trans. Ultras., Ferroel. Freq. Control, 69(7), 2352-2370 https://doi.org/10.1109/tuffc.2022.3177469.