Synchronization of reaction-diffusion delayed inertial memristive neural networks via adaptive pinning control.

The synchronization control problem of delayed inertial memristive neural networks (DIMNNs) with reaction-diffusion terms is addressed. First, by differential inclusions and a reduced-order approach to analyze the DIMNNs. Second, an adaptive pinning control method is introduced to achieve synchronization of drive-and-response systems. By applying inequality technology and Green's Formula, a criterion is obtained to ensure the synchronization of DIMNNs with reaction-diffusion terms. Furthermore, the proposed control scheme requires fewer controlled nodes compared to the full-state feedback method, exhibits robustness against parameter uncertainties, and automatically adapts to varying network conditions. Finally, a numerical example is presented to confirm the theoretical results and demonstrate the effectiveness of the proposed approach.