Exploring Fixed-Time Synchronization of Fractional-Order Fuzzy Cellular Neural Networks with Information Interactions and Time-Varying Delays via Adaptive Multi-Module Control

This article focuses on the fixed-time synchronization problem for fractional-order fuzzy cellular neural networks (FOFCNNs) with information interactions and time-varying delays. To capture the complex dynamics of practical networks, nonlinear activation functions along with fuzzy AND and OR operators are incorporated into the master–slave systems. To achieve fixed-time synchronization despite these complexities, a novel adaptive multi-module controller is proposed. This controller integrates three functionally distinct components to accelerate the convergence rate, eliminate the effects of delays, and introduce negative feedback during communication, respectively. By employing fractional calculus tools, inequality techniques, and the proposed control law, sufficient criteria for the synchronization of the considered systems are rigorously established. Compared with existing synchronization works, this paper has significant advantages in model generality and controller design. Additionally, an explicit settling-time estimate is derived, which depends solely on control parameters and is independent of the initial conditions.