Internal and boundary control-based fixed-time synchronization for stochastic impulsive reaction-diffusion complex networks

This paper focuses on the fixed-time (FXT) synchronization in probability of stochastic impulsive reaction–diffusion complex networks (SIRDCNs) with Robin boundary conditions (RBCs). Firstly, stochastic disturbances and impulsive effects are incorporated into the reaction–diffusion complex networks (RDCNs) to increase the generalization in practical applications. Then, the RBC that generates the Neumann and Dirichlet boundary conditions is employed, which offers greater flexibility than a single-type boundary condition. Subsequently, to achieve FXT synchronization in probability for the addressed SIRDCNs, this paper designs internal and boundary controllers, where the internal controller is implemented over the entire spatial domain, while the boundary controller only needs to be activated at the domain edges, thereby it is more economic and fits well the real application scenarios. Furthermore, some novel criteria for FXT synchronization in probability of considered network are derived through the Lyapunov functional method and stochastic analysis. Finally, numerical simulations are performed to verify the validity of the proposed criteria.