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

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Listed:
  • Shahram Rezapour
  • Pushpendra Kumar
  • Vedat Suat Erturk
  • Sina Etemad

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, 2022. "A Study on the 3D Hopfield Neural Network Model via Nonlocal Atangana–Baleanu Operators," Complexity, John Wiley & Sons, vol. 2022(1).
    • Handle: RePEc:wly:complx:v:2022:y:2022:i:1:n:6784886
    DOI: 10.1155/2022/6784886
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    References listed on IDEAS

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    1. Hu, Taotao & He, Zheng & Zhang, Xiaojun & Zhong, Shouming, 2020. "Finite-time stability for fractional-order complex-valued neural networks with time delay," Applied Mathematics and Computation, Elsevier, vol. 365(C).
    2. Mohammadi, Hakimeh & Kumar, Sunil & Rezapour, Shahram & Etemad, Sina, 2021. "A theoretical study of the Caputo–Fabrizio fractional modeling for hearing loss due to Mumps virus with optimal control," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).
    3. Kumar, Pushpendra & Erturk, Vedat Suat & Murillo-Arcila, Marina, 2021. "A complex fractional mathematical modeling for the love story of Layla and Majnun," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).
    4. Hashem Najafi & Sina Etemad & Nichaphat Patanarapeelert & Joshua Kiddy K. Asamoah & Shahram Rezapour & Thanin Sitthiwirattham, 2022. "A Study on Dynamics of CD4 + T-Cells under the Effect of HIV-1 Infection Based on a Mathematical Fractal-Fractional Model via the Adams-Bashforth Scheme and Newton Polynomials," Mathematics, MDPI, vol. 10(9), pages 1-32, April.
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