Lagrange stability criteria for hypercomplex neural networks with time varying delays

Abstract

This article deals with the Lagrange stability (LS) of hypercomplex neural networks (HCNNs) with time-varying delays. To overcome the non-commutativity and non-associativity of HCNNs, the HCNNs are separated into equivalent n+1 real-valued neural networks (RVNNs). Then, by Lyapunov theory, LS and the globally attractive exponential set are obtained. Since there are no assumptions about the number of equilibria, these results can also be used to evaluate monostable, multistable, and higher neural networks. Since, complex-valued neural networks (CVNNs), quaternion-valued neural networks (QVNNs), and octonion-valued neural networks (OVNNs), etc., are the particular cases of the HCNNs, therefore our results are more general. Finally, three numerical examples for CVNNs, QVNNs, and OVNNs are provided and analyzed to validate the obtained results.