Multi-stability analysis of fractional-order quaternion-valued neural networks with time delay
Kathiresan S. Kashkynbayev A. Janani K. Rakkiyappan R.
2022American Institute of Mathematical Sciences
AIMS Mathematics
2022#7Issue 33603 - 3629 pp.
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.
Caputo fractional derivative , Fractional-order , Multiple stability , Quaternion-valued neural networks , Time delay
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Department of Mathematics, Rathinam College of Arts and Science, Coimbatore, Tamilnadu, 641021, India
Department of Mathematics, Nazarbayev University, Nur-Sultan, 010000, Kazakhstan
Department of Mathematics, Bharathiar University, Coimbatore, Tamilnadu, 641046, India
Department of Mathematics
Department of Mathematics
Department of Mathematics
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