时滞和扩散驱动下信息物理融合系统恶意病毒传播动力学

本文提出了信息物理融合系统(CPS)中具有反应扩散效应的时滞恶意病毒传播模型, 研究了恶意病毒传播 的空间格局动态演化机制, 为恶意病毒在信息物理融合系统中预测和控制提供了战略指导. 给出了模型的基本再 生产数, 并分析了空间中无病毒平衡点和地方病毒平衡点的存在性. 在无时滞条件下建立了扩散引发的图灵不稳 定条件; 在有时滞条件下得到了时滞依赖的稳定性条件和Hopf分岔判据. 最后, 通过数值仿真验证了理论分析的正 确性.

Dynamics of malicious virus propagation in cyber physical systems driven by time-delay and diffusion

In this paper, a time-delay malicious virus propagation model with reaction-diffusion effect in cyber physical systems (CPS) is proposed, and the spatial pattern dynamic evolution mechanism of malicious virus propagation is studied, which provides a strategic guidance for the prediction and control of malicious virus in cyber physical systems. The basic reproduction number of the reaction-diffusion model is given, and the existence of virus-free equilibrium and local virus equilibrium in space is analyzed. The Turing instability condition caused by diffusion is established without time delay. The delay dependent stability condition and the Hopf bifurcation criterion are obtained. Finally, the correctness of the theoretical analysis is verified by numerical simulations.