Synchronization of Networked Reaction-Diffusion Nonlinear Systems via Hybrid Control

This paper addresses the asymptotic synchronization problem for networked nonlinear reaction–diffusion systems under a novel hybrid control strategy. The hybrid controller consists of two components: impulsive control and continuous feedback control. By combining the comparison principle of impulsive systems with the introduction of a time-varying function and a power exponent to flexibly adjust the system, sufficient conditions for synchronization of networked nonlinear reaction–diffusion systems are derived, ensuring that the error dynamics between the network nodes converge to zero. Numerical simulations of a representative example are presented to demonstrate the practical validity and effectiveness of the proposed theoretical control scheme, confirming that the hybrid controller successfully achieves synchronization.