Stability Analysis of Quaternion-Valued Neutral Neural Networks with Generalized Activation Functions

The article delves into the stability analysis of quaternion-valued neural networks (QVNNs) with neutral terms, highlighting the direct quaternion method as a more natural and compact approach. It extends reciprocally convex inequality and Wirtinger-based inequality to the quaternion domain, deriving less conservative stability conditions. The research removes conventional constraints on neutral activation functions, ensuring more practical and realistic models. The paper also discusses the limitations of traditional decomposition methods and the significance of the direct quaternion approach in handling indivisible activation functions. The theoretical results are validated through a numerical example, demonstrating the global asymptotic stability of the QVNN model. This work paves the way for further exploration of other dynamic properties of QVNNs, such as synchronization and state estimation.