TY - JOUR
T1 - Multi-stability analysis of fractional-order quaternion-valued neural networks with time delay
AU - Kathiresan, S.
AU - Kashkynbayev, Ardak
AU - Janani, K.
AU - Rakkiyappan, R.
N1 - Funding Information:
The work of Ardak Kashkynbayev was supported by the Science Committee of the Ministry of Education and Science of the Republic of Kazakhastan grant OR11466188 “Dynamical Analysis and Synchronization of Complex Neural Networks and its Applications”.
Publisher Copyright:
© 2022 the Author(s), licensee AIMS Press.
PY - 2022
Y1 - 2022
N2 - 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 (2KRp + 1)n, (2KIp + 1)n, (2KJp + 1)n, (2KKp + 1)n equilibrium points, in which [(KRp + 1)]n, [(KIp + 1)]n, [(KJp + 1)]n, [(KKp + 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.
AB - 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 (2KRp + 1)n, (2KIp + 1)n, (2KJp + 1)n, (2KKp + 1)n equilibrium points, in which [(KRp + 1)]n, [(KIp + 1)]n, [(KJp + 1)]n, [(KKp + 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.
KW - Caputo fractional derivative
KW - Fractional-order
KW - Multiple stability
KW - Quaternion-valued neural networks
KW - Time delay
UR - http://www.scopus.com/inward/record.url?scp=85120643388&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85120643388&partnerID=8YFLogxK
U2 - 10.3934/math.2022199
DO - 10.3934/math.2022199
M3 - Article
AN - SCOPUS:85120643388
SN - 2473-6988
VL - 7
SP - 3603
EP - 3629
JO - AIMS Mathematics
JF - AIMS Mathematics
IS - 3
ER -