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Attractiveness of pseudo almost periodic solutions for delayed cellular neural networks in the context of fuzzy measure theory in matrix-valued fuzzy spaces

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Abstract

In this paper, considering fuzzy measure theory and matrix-valued fuzzy norm spaces, we study a differential system of non-autonomous cellular neural networks with mixed delays (NA-CNN-MD). Our main goal is to investigate the existence of a unique solution for the presented system of NA-CNN-MD in the matrix-valued fuzzy spaces and using the fuzzy measure. After investigating the existence of a unique solution of NA-CNNs-MD which are \(\varrho \)-pseudo almost periodically, we prove the Mittag–Leffler stability and Mittag-Leffler attractiveness for \(\varrho \)-pseudo almost periodic functions. Finally, two examples are given to illustrate the theoretical results.

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References

  • Ait Dads E, Arino O (1996) Exponential dichotomy and existence of pseudo almost-periodic solutions of some differential equations. Nonlinear Anal 27(4):369–386

    Article  MathSciNet  MATH  Google Scholar 

  • Bekolle D, Ezzinbi K, Fatajou S, Elvis Houpa Danga D, Mbounja Besseme F (2021) Attractiveness of pseudo almost periodic solutions for delayed cellular neural networks in the context of measure theory. Neurocomputing 435:253–263

    Article  MATH  Google Scholar 

  • Blot J, Cieutat P, Ezzinbi K (2013) New approach for weighted pseudo-almost periodic functions under the light of measure theory, basic results and applications. Appl Anal 92(3):493–526

    Article  MathSciNet  MATH  Google Scholar 

  • Boczek M, Kaluszka M (2016) On the Minkowski-Hölder type inequalities for generalized Sugeno integrals with an application. Kybernetika (Prague) 52(3):329–347

    MathSciNet  MATH  Google Scholar 

  • Caballero J, Sadarangani K (2010) A Cauchy-Schwarz type inequality for fuzzy integrals. Nonlinear Anal 73(10):3329–3335

    Article  MathSciNet  MATH  Google Scholar 

  • Chua LO, Yang Lin (1988a) Cellular neural networks: theory. IEEE Trans Circ Syst 35(10):1257–1272

    Article  MathSciNet  MATH  Google Scholar 

  • Chua LO, Yang L (1988b) Cellular neural networks: applications. IEEE Trans Circ Syst 35(10):1273–1290

    Article  MathSciNet  Google Scholar 

  • Diagana T (2006) Weighted pseudo almost periodic functions and applications. C R Math Acad Sci Paris 343(10):643–646

    Article  MathSciNet  MATH  Google Scholar 

  • Fink AM (1974) Almost periodic differential equations. In: Lecture Notes in Mathematics, vol. 377. Springer-Verlag, Berlin-New York, p viii+336

  • Ghanmi B, Miraoui M (2020) Stability of unique pseudo almost periodic solutions with measure. Appl Math 65(4):421–445

    Article  MathSciNet  MATH  Google Scholar 

  • Jia J, Huang X, Li Y, Cao J, Alsaedi A (2020) Global stabilization of fractional-order memristor-based neural networks with time delay. IEEE Trans Neural Netw Learn Syst 31(3):997–1009

    Article  MathSciNet  Google Scholar 

  • Kaluszka M, Okolewski A, Boczek M (2014) On Chebyshev type inequalities for generalized Sugeno integrals. Fuzzy Sets Syst 244:51–62

    Article  MathSciNet  MATH  Google Scholar 

  • Klement EP, Mesiar R, Pap E (2000) Triangular norms-basic properties and representation theorems. Novák, Vilém (ed.) In: Discovering the world with fuzzy logic, Stud. Fuzziness Soft Comput., 57, Physica, Heidelberg, 63–81

  • Liang J, Xiao T-J, Zhang J (2010) Decomposition of weighted pseudo-almost periodic functions. Nonlinear Anal 73(10):3456–3461

    Article  MathSciNet  MATH  Google Scholar 

  • Li Y, Lü G, Meng X (2019) Weighted pseudo-almost periodic solutions and global exponential synchronization for delayed QVCNNs. In: J. Inequal. Appl. Paper No. 231, 23 pp

  • Liu B (2015a) Pseudo almost periodic solutions for neutral type CNNs with continuously disturbed leakage delays. Neurocomputing 148:445–454

    Article  Google Scholar 

  • Liu B (2015b) Exponential convergence of SICNNs with delays and oscillating coefficients in leakage terms. Neurocomputing 168:500–504

    Article  Google Scholar 

  • Liu B (2016) Global exponential convergence of non-autonomous cellular neural networks with multi-proportional delays. Neurocomputing 191:352–355

    Article  Google Scholar 

  • Liu B, Tunc C (2015) Pseudo almost periodic solutions for CNNs with leakage delays and complex deviating arguments. Neural Comput Appl 26:429–435

    Article  Google Scholar 

  • Mainardi F (2010) Fractional calculus and waves in linear viscoelasticity. An introduction to mathematical models. Imperial College Press, London, p xx+347 (pp. ISBN: 978-1-84816-329-4, 1-84816-329-0)

    Book  MATH  Google Scholar 

  • Miraoui M, Yaakoubi N (2019) Measure pseudo almost periodic solutions of shunting inhibitory cellular neural networks with mixed delays. Numer Funct Anal Optim 40(5):571–585

    Article  MathSciNet  MATH  Google Scholar 

  • N’Guërëkata Gaston M (2005) Topics in almost automorphy. Springer-Verlag, New York, p xii+168 (ISBN: 0-387-22846-2)

    MATH  Google Scholar 

  • Pap E (1995) Null-additive set functions. In: Mathematics and its applications, 337. Kluwer Academic Publishers Group, Dordrecht, Ister Science, Bratislava, p xii+315 (ISBN: 0-7923-3658-5)

  • Podlubny I (1999) Fractional differential equations. An introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications. In: Mathematics in science and engineering, 198. Academic Press, Inc., San Diego, pp xxiv+340, (ISBN: 0-12-558840-2)

  • Ralescu D, Adams G (1980) The fuzzy integral. J Math Anal Appl 75(2):562–570

    Article  MathSciNet  MATH  Google Scholar 

  • Roman-Flores H, Chalco-Cano Y (2007) Sugeno integral and geometric inequalities. Internat J Uncertain Fuzziness Knowl-Based Syst 15(1):1–11

    Article  MathSciNet  MATH  Google Scholar 

  • Royden HL (1988) Real analysis, 3rd edn. Macmillan Publishing Company, New York, p xx+444 (ISBN: 0-02-404151-3)

    MATH  Google Scholar 

  • Rudin W (1986) Analiza rzeczywista i zespolona. (Polish) [[Real and complex analysis]] Translated from the English by Antoni Pierzchalski and Paweł Walczak. Państwowe Wydawnictwo Naukowe (PWN), Warsaw, p 432 (ISBN: 83-01-05124-8)

    Google Scholar 

  • Wang ZY, Klir GJ (1992) Fuzzy measure theory. Plenum Press, New York, p x+354 (ISBN: 0-306-44260-4)

    Book  MATH  Google Scholar 

  • Xu J (2018) Weighted pseudo almost periodic delayed cellular neural networks. Neural Comput Appl 30:2453–2458

    Article  Google Scholar 

  • Yan Z, Huang X, Fan Y, Xia J, Shen H (2020) Threshold-function-dependent quasisynchronization of delayed memristive neural networks via hybrid eventtriggered control. IEEE Trans Syst Man Cybernet Syst. https://doi.org/10.1109/TSMC.2020.2964605

    Article  Google Scholar 

  • Yao L, Wang Z, Huang X, Li Y, Shen H, Chen G (2020) A periodic sampled-data control for exponential stabilization of delayed neural networks: a refined two-sided lopped-functional approach, IEEE Trans. Circ Syst-II EXPRESS BRIEFS. https://doi.org/10.1109/TCSII.2020.2983803

    Article  Google Scholar 

  • Yu Y (2017) Exponential stability of pseudo almost periodic solutions for cellular neural networks with multi-proportional delays. Neural Process Lett 45:141–151

    Article  Google Scholar 

  • Yu CH (2022) A study of some fractional functions. Int J Math Trends Technol (IJMTT) 66

  • Zhang CY (1994a) Integration of vector-valued pseudo-almost periodic functions. Proc Am Math Soc 121(1):167–174

    Article  MathSciNet  MATH  Google Scholar 

  • Zhang CY (1994b) Pseudo-almost-periodic solutions of some differential equations. J Math Anal Appl 181(1):62–76

    Article  MathSciNet  MATH  Google Scholar 

  • Zhang H (2014) Existence and stability of almost periodic solutions for CNNs with continuously distributed leakage delays. Neural Comput Appl 24:1135–1146

    Article  Google Scholar 

  • Zhang A (2017) Pseudo almost periodic solutions for SICNNs with oscillating leakage coefficients and complex deviating arguments. Neural Process Lett 45:183–196

    Article  Google Scholar 

  • Zhou Q, Shao J (2018) Weighted pseudo-anti-periodic SICNNs with mixed delays. Neural Comput Appl 29:865–872

    Article  Google Scholar 

Download references

Acknowledgements

The authors are thankful to the area editor and referees for giving valuable comments and suggestions.

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Author notes

  1. Reza Saadati, Tofigh Allahviranloo have contributed equally to this work.

Authors and Affiliations

  1. School of Mathematics, Iran University of Science and Technology, Narmak, Tehran, Iran

    Zahra Eidinejad & Reza Saadati

  2. Faculty of Engineering and Natural Sciences, Istinye University, Istanbul, Turkey

    Tofigh Allahviranloo

Authors
  1. Zahra Eidinejad
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  2. Reza Saadati
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  3. Tofigh Allahviranloo
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Correspondence to Reza Saadati or Tofigh Allahviranloo.

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Communicated by Susana Montes.

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Eidinejad, Z., Saadati, R. & Allahviranloo, T. Attractiveness of pseudo almost periodic solutions for delayed cellular neural networks in the context of fuzzy measure theory in matrix-valued fuzzy spaces. Comp. Appl. Math. 41, 369 (2022). https://doi.org/10.1007/s40314-022-02074-z

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  • DOI: https://doi.org/10.1007/s40314-022-02074-z

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