@article{Ke2024, 
author = {Jiang-Wei Ke and Jin-E Zhang},
title = {Associative memories based on delayed fractional-order neural networks and application to explaining-lesson skills assessment of normal students: from the perspective of multiple        O    (      t          −      α        ) stability},
year = {2024},
journal = {AIMS Mathematics},
volume = {9},
number = {7},
pages = {17430-17452},
keywords = {associative memory, fractional-order neural networks, multiple O(t−α) stability, piecewise nonlinear activation functions, time-varying delays},
url = {https://www.sciopen.com/article/10.3934/math.2024847},
doi = {10.3934/math.2024847},
abstract = {This paper discusses associative memories based on time-varying delayed fractional-order neural networks (DFNNs) with a type of piecewise nonlinear activation function from the perspective of multiple        O    (      t          −      α        ) stability. Some sufficient conditions are gained to assure the existence of        5    n   equilibria for    n-neuron DFNNs with the proposed piecewise nonlinear activation functions. Additionally, the criteria ensure the existence of at least        3    n   equilibria that are locally multiple        O    (      t          −      α        ) stable. Furthermore, we apply these results to a more generic situation, revealing that DFNNs can attain    (  2  k  +  1      )    n   equilibria, and among them,    (  k  +  1      )    n   equilibria are locally        O    (      t          −      α        ) stable. Here, the parameter    k is highly dependent on the sinusoidal function frequency in the expanded activation functions. Such DFNNs are well-suited to synthesize high-capacity associative memories; the design process is given via singular value decomposition. Ultimately, four illustrative examples, including applying neurodynamic associative memory to the explaining-lesson skills assessment of normal students, are supplied to validate the efficacy of the results.}
}