<p>Traditionally, the spatiotemporal dynamics of neural networks have been analyzed in the locally continuous domain. While this modeling approach is straightforward and practical, it fails to encapsulate real-world networks’ intricate topological structures and evolution. Currently, the mechanisms of stability switches induced by time delays and diffusion effects in network-organized systems are still vague. Besides, effective dynamic optimization strategies for network-organized models remain to be devised. In this study, we develop a delayed reaction-diffusion neural network model on complex networks. This system incorporates the effects of inter-nodal diffusion coupling and exhibits profound architectural complexity. We then pioneer the proportional-integral-derivative (PID) feedback control into the network-organized model to modulate dynamic behaviors. The linear stability analysis is conducted firstly, demonstrating that Turing patterns and Hopf bifurcation can be induced in the controlled neural network by varying diffusion coefficients and time delays. Subsequently, the bifurcation direction is deduced via the center manifold theorem. Finally, a series of simulations are performed to validate the theoretical analysis and substantiate the efficacy of the PID control strategy. The results exhibit that the PID feedback controller can flexibly regulate the dynamics of the network-organized systems and possesses excellent disturbance rejection capabilities.</p>