Fast fixed-/preassigned-time synchronization of Clifford-valued neural networks for medical image encryption

This paper aims to investigate the fixed-time (FXT) and preassigned-time (PAT) synchronization for Clifford-valued neural networks (CFVNNs) with mixed delays by improving a novel FXT stability theorem and using non-decomposing two-step method. First of all, a novel FXT stability theorem has been derived. Its time estimation formula and settling time are simpler and accurate compared to existing stability theorem. Then, based on this novel FXT stability theorem, the FXT synchronization of the CFVNNs is obtained by designing sample nonlinear controller and Lyapunov function and seeking the settling time. As a special case, the PAT synchronization of CFVNNs is investigated, in which the estimation of settling time is independent of any initial conditions of neural networks and any parameters of the designed controllers. Lastly, numerical examples demonstrate the effectiveness and superiority of the derived theoretical results. The research also extends to the practical domain, evaluating the impact of CFVNNs and the designed controllers on medical image encryption.