Fixed-time synchronization of delayed multiple inertial neural network with reaction-diffusion terms under cyber–physical attacks using distributed control and its application to multi-image encryption

This study examines the fixed-time synchronization (FXTS) problem of delayed multiple inertial neural networks (MINNs) against cyber–physical attacks (CPA) execute an uncertain impulse, using reaction–diffusion (RD) terms. Using fixed-time stability theory, the paper derives innovative and practical criteria for FXTS. It also introduces a MINNs to counteract CPA by executing uncertain impulses with RD terms. Designing security control laws for MINNS with RD terms poses significant challenges, particularly when these networks are tasked with cooperative functions in the presence of failures or attacks. A distributed control strategy is introduced to attain FXTS for the delayed MINNs incorporating RD terms. To examine the consequences of CPA, we will build a Lyapunov function and combine it with some M-matrix properties. Additionally, a security control law is provided to guarantee the FXTS of the consider NN system. The demonstrated settling time (ST) of the designated MINNs is provided. From an algorithmic perspective, it is notable that the security framework and control algorithm are designed to select parameters for the feedback gain matrix and coupling strength to achieve synchronization. A numerical model is provided to support the obtained theoretical findings. Finally, our proposition of a multi-image encryption algorithm, utilizing MINNs and secured by robust security protocols, serves to uphold the integrity of electronic healthcare systems, ensuring the safeguarding of sensitive medical data.