Coexistence of locally multistable equilibrium points for [formula omitted]-neuron delayed quaternion-valued neural networks with continuous piecewise nonlinear activation functions

Abstract

This article investigates the coexistence of multistable equilibrium points (EPs) for n-neuron delayed quaternion-valued neural networks (DQVNNs) in which the continuous and piecewise nonlinear functions are used as the activation functions. Using the state space decomposition technique, Brouwer’s fixed point theorem, and Lagrange’s mean value theorem, some novel sufficient conditions have been derived to ensure the coexistence of 54n EPs in which 34n of them are locally stable. Furthermore, in this scientific contribution, positively invariant sets have been estimated which actually turned out to be quite challenging for the activation functions of the designed DQVNNs. Finally, some comparisons and convincing simulations with the application to associative memory of DQVNNs are given to verify the theoretical results at the end of this article.