Design of deep learning networks for nonlinear delay differential system for Stuxnet virus spread in an air gapped critical environment

Within the tranquil confines of air-gapped environment, the custodians of digital fortitude must recognize the limitations of a singular defense mechanism, the cornerstone of this defensive architecture lies in proactive threat detection and rapid response capabilities. In the presented study, a deep-learning based bidirectional LSTM architecture is designed to accurately capture the time-delay differential propagation dynamics of the Stuxnet virus in an air gapped environment intricately linked with a network of critical control infrastructure. To address the challenges encountered in compromising the air gapped environment, the mathematical model introduces time delay factors ${\tau }_1$, ${\tau }_2$ and ${\tau }_3$, necessary for exploiting the susceptible USB media, susceptible air gapped computers utilizing infected USB media and connected susceptible computers using infected computers respectively. Removable storage media serves as a pivotal link in bridging the air gapped environment and controlling the industrial controllers connected to critical systems thereby posing a significant threat to the integrity of the entire system. Synthetic temporal simulations serve as the ground truth for dual-layer bidirectional LSTM networks exactment on various scenarios involving the infiltration of the air-gapped environment by the Stuxnet virus in a time delay differential system. A detailed comparative analysis with numerical outcomes showed minimal disparity between the predictions generated by LSTM networks, with mean squared error (MSE) values falling within the range of $10^{-7}$ underscoring the effectiveness, robustness, and stability of the proposed neural networks in predicting the complex dynamics of virus in air gapped situation.