Stability and Synchronization of Delayed Quaternion-Valued Neural Networks under Multi-Disturbances

Abstract

This paper discusses a type of mixed-delay quaternion-valued neural networks (QVNNs) under impulsive and stochastic disturbances. The considered QVNNs model are treated as a whole, rather than as complex-valued neural networks (NNs) or four real-valued NNs. Using the vector Lyapunov function method, some criteria are provided for securing the mean-square exponential stability of the mixed-delay QVNNs under impulsive and stochastic disturbances. Furthermore, a type of chaotic QVNNs under stochastic and impulsive disturbances is considered using a previously established stability analysis method. After the completion of designing the linear feedback control law, some sufficient conditions are obtained using the vector Lyapunov function method for determining the mean-square exponential synchronization of drive–response systems. Finally, two examples are provided to demonstrate the correctness and feasibility of the main findings and one example is provided to validate the use of QVNNs for image associative memory.

Performance Evaluation of Railway Infrastructure Managers: A Novel Hybrid Fuzzy MCDM Model

“…The issue discussed in this research could potentially be resolved through different methods. These may involve using simulations of diverse scenarios (e.g., [35]), optimization models offering mathematical frameworks to systematically identify the best possible solutions given specific constraints and objectives (e.g., [36]), metaheuristic algorithms to effectively explore solution spaces (e.g., [37]), and artificial intelligence methods like neural networks to analyze intricate datasets (e.g., [38]). Each method presents distinct advantages, from offering insights into potential results to utilizing large data sets for predictive analysis.…”