Multistability analysis of octonion-valued neural networks with time-varying delays

Abstract

In this article, the multistability analysis is studied for n-dimensional octonion valued neural networks (OVNNs) with time-varying delays for a general class of activation functions. Firstly, OVNNs are decomposed into eight real-valued systems, and then based on geometrical properties of activation functions, 38n disjoint regions are constructed in On. Then, by using the inequality technique, several sufficient conditions are obtained to ensure the existence of 38n equilibrium points of the system, each of which is located in one of the regions, and 28n of them are locally exponentially stable. Moreover positively invariant sets are also estimated in this scientific contribution. Two numerical examples are provided to illustrate the effectiveness of the obtained results. Especially, the numerical Example 2 demonstrates that the designed OVNNs work efficiently on storing and retrieving the truecolor images. © 2022