Stability analysis of quaternion-valued BAM neural networks fractional-order model with impulses and proportional delays

In this paper, a class of quaternion-valued BAM neural networks (QVBAMNNs) fractional-order model with impulses and proportional delays is proposed in discrete-time case. The QVBAMNNs fractional -order model is investigated directly rather than through real decomposition method or the plural one. By employing homeomorphic mapping theorem, Lyapunov stability theory and inequality technology, several criteria for the discrete-time QVBAMNNs fractional-order model are derived to guarantee the existence, uniqueness and global exponential stability (GES) of equilibrium point. The novelty of these results comes from the generality with the fractional-order systems and the integer-order ones. Finally, two examples are given to demonstrate the effectiveness and availability of the derived criteria.(c) 2022 Elsevier B.V. All rights reserved.

Automated summary

This paper proposes a fractional-order model of quaternion-valued BAM neural networks (QVBAMNNs) with impulses and proportional delays in discrete-time case, and derives several criteria for the existence, uniqueness, and global exponential stability (GES) of equilibrium point by employing the homeomorphic mapping theorem, Lyapunov stability theory, and inequality technology. The novelty of these results lies in their generality for both fractional-order systems and integer-order ones.