Journal of the Chungcheong Mathematical Society (충청수학회지)

The Chungcheong Mathematical Society (충청수학회)
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STEPANOV ALMOST PERIODIC SOLUTIONS OF CLIFFORD-VALUED NEURAL NETWORKS

  • Lee, Hyun Mork (Department of Applied Mathematics Kongju National University)
  • Received : 2022.01.29
  • Accepted : 2022.02.16
  • Published : 2022.02.15
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Abstract

We introduce Clifford-valued neural networks with leakage delays. Furthermore, we study the uniqueness and existence of Clifford-valued Hopfield artificial neural networks having the Stepanov weighted pseudo almost periodic forcing terms on leakage delay terms. However the noncommutativity of the Clifford numbers' multiplication made our investigation diffcult, so our results are obtained by decomposing Clifford-valued neural networks into real-valued neural networks. Our analysis is based on the differential inequality techniques and the Banach contraction mapping principle.

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References

  1. C, Bai. Existence and stability of almost periodic solutions of Hopfield neural networks with continuously distributed delays, Nonlinear Anal., 71 (2009), no. 11, 5850-5859. https://doi.org/10.1016/j.na.2009.05.008
  2. J. Blot ,P. Cieutat,G. M. N'Guerekata and D. Pennequin, Superposition operators between various almost periodic function spaces and applications, Commun. Math. Anal., 6 (2000), no.1, 42-70.
  3. F. Cherif, M. Abdelaziz, Stepanov-Like Pseudo Almost Periodic Solution of Quaternion-Valued for Fuzzy Recurrent Neural Networks with Mixed Delays, Neural Process. Lett., 51 (2020), no. 3, 2211-2243. https://doi.org/10.1007/s11063-020-10193-z
  4. T. Diagana, G. M. Mophou and G. M. N'Guerekata, Existence of weighted pseudo-almost periodic solutions to some classes of differential equations with Sp-weighted pseudo-almost periodic coefficients, Nonlinear Anal., 72 (2010), no. 1, 430-438. https://doi.org/10.1016/j.na.2009.06.077
  5. A. M. Fink, Almost periodic differential equations, Lecture notes in mathematics, Springer Berlin, 377 (1974).
  6. A. N. Kolmogorov, On the representation of continuous functions of many variables by supetposition of continuous functions one variable andaddition, Doklady Akademmi Nauk SSSE, 114 (1957), 953-956.
  7. H.M. Lee, Weighted pseudo almost periodic solutions of Hopfield artificial neural networks with leakage delay terms, J. Chungcheong Math. Soc., 34 (2021), no. 3, 221-234. https://doi.org/10.14403/JCMS.2021.34.3.221
  8. B. Li and Y. Li, Existence and Global Exponential Stability of Pseudo Almost Periodic Solution for Clifford-Valued Neutral High-Order Hopfield Neural Networks With Leakage Delays, IEEE., (2019).
  9. Y. Li and X. Meng, Almost Automorphic Solutions for Quaternion-Valued Hopfield Neural Networks with Mixed Time-Varying Delays and Leakage Delays, J. Syst. Sci. Complex., 33 (2020), 100-121. https://doi.org/10.1007/s11424-019-8051-1
  10. M, Maqbul, Stepanov-almost periodic solutions of non-autonomous neutral functional differential equations with functional delay, Mediterr. J. Math., 15 (2018), no. 4.
  11. Y. Li and J. Xiang, Existence and global exponential stability of anti-periodic solution for clifford-valued inertial cohengrossberg neural networks with delays, Neuro computing, 332 (2019), no. 2, 259-269.
  12. Y. Xu, Weighted pseudo-almost periodic delayed cellular neural networks, Neural Comput. Appl., 30 (2018), no. 10, 2453-2458. https://doi.org/10.1007/s00521-016-2820-8
  13. G. Rajchakit and R, Siraman, Robust passivity and stability analysis of uncertain complex-valued impulsive neural networks with time-varing delays, Neural Process. Lett., 53 (2021), no. 13, 581-606. https://doi.org/10.1007/s11063-020-10401-w
  14. S. Shen and Y. Li, Sp-Almost Periodic Solutions of Clifford-Valued Fuzzy Cellular Neural Networks with Time-Varying Delays, Neural Process. Lett., 51 (2020), no. 2, 1749-1769. https://doi.org/10.1007/s11063-019-10176-9
  15. H. Wang and G. Wei, S. Huang, Impulsive disturbance on stability analysis of delayed quaternion-valued neural networks, Appl. Math. Comptu., 390 (2021), no. 12, 125680. https://doi.org/10.1016/j.amc.2020.125680
  16. G. Yang and W. Wan, Weighted Pseudo Almost Periodic Solutions for Cellular Neural Networks with Multi-proportional Delays, Neural Process. Lett., 49 (2019), no. 3, 1125-1138. https://doi.org/10.1007/s11063-018-9851-3
  17. Z. Zhao, Y. Chang and G.M. N'Guerekata, A new composition theorem for Sp-weighted pseudoalmostperiodic functions and applications to semilinear differential equattions, Opuscula Mathematica. 31 (2011), no. 3, 457-474. https://doi.org/10.7494/OpMath.2011.31.3.457