Robust stability analysis of quaternion-valued neural networks with time delays and parameter uncertainties

Stability analysis of quaternion‐valued Cohen‐Grossberg neural networks

“…Lemma (Chen et al) If is a continuous map and satisfies the following conditions: H ( x ) is injective on ; , then, H ( x ) is a homeomorphism of onto itself.…”

“…Very recently, the quaternion‐valued neural networks (QVNNs) are obtained by modifying the states, connection weights, together with the activation functions, in which these parameters are quaternion vectors or matrices. This kind of system is taken as an extension of the quaternion theory, and some related works can be found in Tu et al, Song and Chen, Chen, Song, et al, and Chen, Li, et al() Among which, the dissipativity analysis for QVNNs are considered in Tu et al, the corresponding stability including multistability analysis of QVNNs are given in Chen et al, Hu and Wang, Fang and Sun, and Khalil. () Khalil paid attention to the multistability issues of QVNNs, subsequently, an interesting works concentrated on both the continuous‐time and discrete‐time QVNNs are available in Chen, Song, et al, and a thorough inquiry of the stability analysis of QVNNs with uncertain parameters were made by Chen, Li, et al…”

Almost Periodic Synchronization for Quaternion‐Valued Neural Networks with Time‐Varying Delays

“…In recent years, the quaternion-valued neural networks, as an extension of the real-valued neural networks and the complex-valued neural networks [6,7], research has become a hot topic. It should be pointed out that, at present, almost all the investigations on quaternion-valued neural networks are mainly dealing with the stability, robustness, or dissipation of the equilibrium of the neural networks; see [8][9][10][11][12][13][14][15][16][17].…”

Anti-Periodic Dynamics of Quaternion-Valued Fuzzy Cellular Neural Networks with Time-Varying Delays on Time Scales

“…On the one hand, because quaternion-valued neural networks (QVNNs) as an extension of the real-valued neural networks and complex-valued neural networks can be extensively applied to the fields of robotics, attitude control of satellites, computer graphics, ensemble control, color night vision, and image compression ( [12][13][14]) and one of the benefits by using quaternion is the three-dimensional geometrical affine transformation that can be represented efficiently and compactly, the study of dynamical behaviors for QVNNs has received much attention of many scholars and some good results have been obtained for the stability [15][16][17][18][19], dissipativity [20], periodicity [21], pseduo almost periodicity [22], and synchronization of QVNNs [23,24].…”