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WEIGHTED PSEUDO ALMOST PERIODIC SOLUTIONS OF HOPFIELD ARTIFICIAL NEURAL NETWORKS WITH LEAKAGE DELAY TERMS

  • Lee, Hyun Mork (Department of Applied Mathematics Kongju National University)
  • Received : 2021.05.11
  • Accepted : 2021.07.05
  • Published : 2021.08.15

Abstract

We introduce high-order Hopfield neural networks with Leakage delays. Furthermore, we study the uniqueness and existence of Hopfield artificial neural networks having the weighted pseudo almost periodic forcing terms on finite delay. Our analysis is based on the differential inequality techniques and the Banach contraction mapping principle.

Keywords

References

  1. A. Alimi, C. Aouiti, F. Cherif, F. Dridi, M. M'hamdi, Dynamics and oscillations of generalized high-order neural networks with mixed delays, Neurocomputing. 321 (2018), 274-295. https://doi.org/10.1016/j.neucom.2018.01.061
  2. C. Aouiti, M. M'hamdi, F. Cherif, The existence and the stability of weighted pseudo almost periodic solution of high-order Hopfield neural network, Springer International Publishing Switzerland. (2016), 478-485.
  3. C. Aouiti, M. M'hamdi, A. Touati, Pseudo almost automorphic solutions of recurrent neural networks with time-varying coefficients and mixed delays, Neural Process Lett. 45 (2017), 121-140. https://doi.org/10.1007/s11063-016-9515-0
  4. C. Bai, Existence and stability of almost periodic solutions of Hopfield neural networks with continuously distributed delays, Nonlinear Anal., 71 (2012), no. 11, 5850-5859. https://doi.org/10.1016/j.na.2009.05.008
  5. T. Diagana, Almost Automorphic Type and Almost Periodic Type Functions in Abstract Spaces, Springer International Publishing Switzerland. 2013.
  6. J. Hopfield, Neurons with graded response have collective computational properties like those of two-state neurons, Proc Natl Acad Sci USA., 81 (1984),no. 10, 3088-3092. https://doi.org/10.1073/pnas.81.10.3088
  7. H.M. Lee,Existence of functional differential equations with Stepanov forcing terms, J. Chungcheong Math. Soc,. 33 (2020), no.3, 351-363. https://doi.org/10.14403/JCMS.2020.33.3.351
  8. Y. Li, L. Zhao, X. Chen, Existence of periodic solutions for neutral type cellular neural networks with delays, Appl. Math. Model., 36 (2012), no. 3, 1173-1183. https://doi.org/10.1016/j.apm.2011.07.090
  9. F. Qiu, B. Cui, W. Wu, Global exponential stability of high order recurrent neural network with time-varying delays, Appl. Math. Model., 33 (2009), no. 1, 198-210 https://doi.org/10.1016/j.apm.2007.10.021
  10. W. Wang, B. Liu Global exponential stability of pseudo almost periodic solutions for SICNNs with time-varing leakage delays, Abstr. Appl. Anal., 31 (2014), 1-17.
  11. B. Xiao, Existence and uniqueness of almost periodic solutions for a class of Hopfield neural networks with neutral delays, Appl. Math. Lett., 22 (2009), no. 4, 528-533. https://doi.org/10.1016/j.aml.2008.06.025
  12. C. Xu, P. Li, Pseudo almost periodic solutions for high-order Hopfield neural networks with time-varing leakage delays, Neural Processes Lett. 46 (2017), 41-58. https://doi.org/10.1007/s11063-016-9573-3
  13. H. Yang, Weighted pseudo almost periodicity on neutral type CNNs involving multi-proportional delays and D operator, AIMs Mathematics. 6 (2020) ,no. 2, 1865-1879. https://doi.org/10.3934/math.2021113
  14. C. Zhang, Almost Periodic Type Functions and Ergodicity, Science Press, Beijing. 2003.
  15. L. Zhao, Y. Li, Global exponential stability of weighted pseudo almost periodic solutions of neutral type high-order Hopfield neural networks with distributed delays, Abstr. Appl. Anal., 2014 (2014), 1-17.