Fixed-time synchronization of mixed-delay fuzzy cellular neural networks with $L\acute{e}vy$ noise

In this paper, we investigate the fixed-time synchronization of fuzzy stochastic cellular neural networks (FSCNNs) with mixed delay and $L\acute{e}vy$ noise. We designed the feedback controller and adaptive controller for cellular neural networks with $L\acute{e}vy$ noise to achieve fixed-time synchronization. Using the Lyapunov theory and the $It\hat{o}$ formula, we established the criterion for fixed-time synchronization of FSCNNs with $L\acute{e}vy$ noise. Additionally, we obtained the resulting settling time, which is independent of the initial values of the system. The practicality and validity of the theoretical conclusions are demonstrated through two examples. The research results show that when the intensity of random interference is not large, FSCNNs can achieve synchronization through appropriate control means.