@article{Kathiresan2022, 
author = {S. Kathiresan and Ardak Kashkynbayev and K. Janani and R. Rakkiyappan},
title = {Multi-stability analysis of fractional-order quaternion-valued neural networks with time delay},
year = {2022},
journal = {AIMS Mathematics},
volume = {7},
number = {3},
pages = {3603-3629},
keywords = {multiple stability, fractional-order, caputo fractional derivative, quaternion-valued neural networks, time delay},
url = {https://www.sciopen.com/article/10.3934/math.2022199},
doi = {10.3934/math.2022199},
abstract = {This paper addresses the problem of multi-stability analysis for fractional-order quaternion-valued neural networks (QVNNs) with time delay. Based on the geometrical properties of activation functions and intermediate value theorem, some conditions are derived for the existence of at least    (  2            K        p    R    +  1      )    n    ,  (  2            K        p    I    +  1      )    n    ,  (  2            K        p    J    +  1      )    n    ,  (  2            K        p    K    +  1      )    n   equilibrium points, in which    [  (            K        p    R    +  1  )      ]    n    ,  [  (            K        p    I    +  1  )      ]    n    ,  [  (            K        p    J    +  1  )      ]    n    ,  [  (            K        p    K    +  1  )      ]    n   of them are uniformly stable while the other equilibrium points become unstable. Thus the developed results show that the QVNNs can have more generalized properties than the real-valued neural networks (RVNNs) or complex-valued neural networks (CVNNs). Finally, two simulation results are given to illustrate the effectiveness and validity of our obtained theoretical results.}
}