We model a vehicle equipped with an autonomous cyber-defense system in addition to its inherent physical resilience features. When attacked, this ensemble of cyber-physical features (i.e., ``bonware'') strives to resist and recover from the performance degradation caused by the malware's attack. We model the underlying differential equations governing such attacks for piecewise linear characterizations of malware and bonware, develop a discrete time stochastic model, and show that averages of instantiations of the stochastic model approximate solutions to the continuous differential equation. We develop a theory and methodology for approximating the parameters associated with these equations.

翻译：我们构建了一类配备自主网络防御系统的车辆模型，该车辆同时具备固有的物理弹性特征。当遭受攻击时，这种网络-物理特性组合（即"防御组件"）将协同抵抗并恢复由恶意软件攻击导致的性能退化。我们针对恶意软件与防御组件的分段线性特征，建立了描述此类攻击过程的微分方程模型；同时开发了离散时间随机模型，并证明该随机模型的多实例平均结果能够近似连续微分方程的解。进一步地，我们提出了用于估计这些方程相关参数的理论框架与方法论。