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A Study on the 3D Hopfield Neural Network Model via Nonlocal Atangana–Baleanu Operators

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  • Shahram Rezapour
  • Pushpendra Kumar
  • Vedat Suat Erturk
  • Sina Etemad
  • Xiao Ling Wang

Abstract

Hopfield neural network (HNN) is considered as an artificial model derived from the brain structures and it is an important model that admits an adequate performance in neurocomputing. In this article, we solve a dynamical model of 3D HNNs via Atangana–Baleanu (AB) fractional derivatives. To find the numerical solution of the considered dynamical model, the well-known Predictor-Corrector (PC) method is used. A number of cases are taken by using two different sets of values of the activation gradient of the neurons as well as six different initial conditions. The given results have been perfectly established using the different fractional-order values on the given derivative operator. The objective of this research is to investigate the dynamics of the proposed HNN model at various values of fractional orders. Nonlocal characteristic of the AB derivative contains the memory in the system which is the main motivation behind the proposal of this research.

Suggested Citation

  • Shahram Rezapour & Pushpendra Kumar & Vedat Suat Erturk & Sina Etemad & Xiao Ling Wang, 2022. "A Study on the 3D Hopfield Neural Network Model via Nonlocal Atangana–Baleanu Operators," Complexity, Hindawi, vol. 2022, pages 1-13, July.
    • Handle: RePEc:hin:complx:6784886
    DOI: 10.1155/2022/6784886
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    Cited by:

    1. Admon, Mohd Rashid & Senu, Norazak & Ahmadian, Ali & Majid, Zanariah Abdul & Salahshour, Soheil, 2024. "A new modern scheme for solving fractal–fractional differential equations based on deep feedforward neural network with multiple hidden layer," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 218(C), pages 311-333.
    2. Avcı, İbrahim & Lort, Hüseyin & Tatlıcıoğlu, Buğce E., 2023. "Numerical investigation and deep learning approach for fractal–fractional order dynamics of Hopfield neural network model," Chaos, Solitons & Fractals, Elsevier, vol. 177(C).

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