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

Stability is a central issue in the study of dynamical systems, and quaternion-valued neural networks (QVNNs) perform well in handling the problem involving high-dimension date. The paper is dedicated to investigating the stability problem of QVNNs with neutral delay. In order to accurately estimate the derivative of Lyapunov functional, both reciprocally convex inequality and Wirtinger-based inequality are extended to the quaternion domain. And the direct quaternion method is used to analyze the quaternion-valued neutral neural networks (QVNNNs). Based on the generalized inequalities, the existence, uniqueness, and global stability criteria for QVNNS with several freedom matrices are derived. Concision and compact stability criteria of QVNNNs are established in the form of quaternion-valued LMIs, and the correctness of the theoretical results was verified through a numerical example.