249
Views
4
CrossRef citations to date
0
Altmetric
Original Articles

On the differential equations of recurrent neural networks

, & ORCID Icon
Pages 1385-1407 | Received 06 Dec 2019, Accepted 31 Aug 2020, Published online: 21 Sep 2020

References

  • S. Abbas, L. Mahto, M. Hafayed, and M.A. Alimi, Asymptotic almost automorphic solutions of impulsive neural network with almost automorphic coefficients, Neurocomputing 142 (2014), pp. 326–334. doi: 10.1016/j.neucom.2014.04.028
  • E. Ait Dads, K. Ezzinbi, and M. Miraoui, (μ,ν)-Pseudo almost automorphic solutions for some nonautonomous differential equations, Int. J. Math. 26 (2015), pp. 1–21. doi: 10.1142/S0129167X15500901
  • C. Aouiti and E.A. Assali, Effect of fuzziness on stability of inertial neural networks with mixed delay via non-reduced order method, Int. J. Comput. Math. 4 (2019), pp. 151–170. doi: doi:10.1080/23799927.2019.1685006
  • C. Aouiti, M.S. M'hamdi, and A. Touati, Pseudo almost automorphic solutions of recurrent neural networks with time-varying coefficients and mixed delays, Neural Process. Lett. 45 (2017), pp. 121–140. doi: 10.1007/s11063-016-9515-0
  • C. Bai, Existence and stability of almost periodic solutions of Hopfield neural networks with continuously distributed delays, Nonlinear Anal. 71 (2009), pp. 5850–5859. doi: 10.1016/j.na.2009.05.008
  • J. Blot, P. Cieutat, and K. Ezzinbi, Measure theory and pseudo almost automorphic functions: New developments and applications, Nonlinear Anal.75 (2012), pp. 2426–2447. doi: 10.1016/j.na.2011.10.041
  • F. Chérif, Sufficient conditions for global stability and existence of almost automorphic solution of a class of RNNs, Differ. Equ. Dyn. Syst. 22 (2014), pp. 191–207. doi: 10.1007/s12591-013-0168-4
  • L. Chua and L. Yang, Cellular neural networks: theory, IEEE Trans. Circuits Syst. 35 (1988), pp. 1257–1272. doi: 10.1109/31.7600
  • L. Chua and L. Yang, Cellular neural networks: applications, IEEE Trans. Circuits Syst. 35 (1988), pp. 1273–1290. doi: 10.1109/31.7601
  • F. Colace, V. Loia, and S. Tomasiello, Revising recurrent neural networks from a granular perspective, Appl. Soft Comput. 82 (2019), pp. 105535. doi: 10.1016/j.asoc.2019.105535
  • A. Cutolo, C. De Nicola, R. Manzo et al., Optimal paths on urban networks using travelling times prevision. Modell. Simul. Eng. 2012 (2012 Article ID 564168, 9 pages, ISSN: 1687-5591.
  • T. Diagana, Weighted pseudo almost periodic functions and applications, C. R. Acad. Sci. 343 (2006), pp. 643–646. doi: 10.1016/j.crma.2006.10.008
  • T. Diagana, K. Ezzinbi, and M. Miraoui, Pseudo almost periodic and pseudo almost automorphic solutions to some evolution equations involving theoretical measure theory, CUBO Math. J. 16 (2014), pp. 1–31. doi: 10.4067/S0719-06462014000200001
  • F. Klebaner, Introduction to Stochastic Calculus with Applications. 2nd ed.Imperial College Press, Amazon France, 2005.
  • Y. Li, X. Meng, Almost automorphic solutions in distribution sense of quaternion-valued stochastic recurrent neural networks with mixed time-varying delays. Neural Process. Lett. 51(2) (2020), pp. 1353–1377. doi: 10.1007/s11063-019-10151-4
  • Y. Li, X. Meng, and L. Xiong, Pseudo almost periodic solutions for neutral type high-order Hopfield neural networks with mixed time-varying delays and leakage delays on time scales, Int. J. Mach. Learn. Cybern. 8 (2017), pp. 1915–1927. doi: 10.1007/s13042-016-0570-7
  • M. Miraoui, Existence of µ-pseudo almost periodic solutions to some evolution equations, Math. Method. Appl. Sci. 40 (2017), pp. 4716–4726.
  • M. Miraoui, Pseudo almost automorphic solutions for some differential equations with reflection of the argument, Numer. Func. Anal. Opt. 38 (2017), pp. 376–394. doi: 10.1080/01630563.2017.1279175
  • F. Qiu, B. Cui, and W. Wu, Global exponential stability of high order recurrent neural network with time-varying delays, Appl. Math. Model. 33 (2009), pp. 198–210. doi: 10.1016/j.apm.2007.10.021
  • L. Rarità, C. D'Apice, B. Piccoli, and D. Helbing, Sensitivity analysis of permeability parameters for flows on Barcelona networks, J. Differ. Eqs. 249 (2010), pp. 3110–3131. ISSN: 0022-0396. doi: 10.1016/j.jde.2010.09.006
  • C. Xu and P. Li, Pseudo almost periodic solutions for high-order Hopfield neural networks with time-varying leakage delays, Neural Process. Lett. 46 (2017), pp. 41–58. doi: 10.1007/s11063-016-9573-3
  • A. Zhang, Pseudo almost periodic solutions for SICNNs with oscillating leakage coefficients and complex deviating arguments, Neural Process. Lett. 45 (2017), pp. 183–196. doi: 10.1007/s11063-016-9518-x
  • C.Y. Zhang, Pseudo almost periodic solutions of some differential equations I, J. Math. Anal. Appl. 151 (1994), pp. 62–76. doi: 10.1006/jmaa.1994.1005

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.