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  

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

作　　者：庄乾辉 肖敏 王赫 邱建龙 梁金玲 蒋海军[4] ZHUANG Qian-hui;XIAO Min;WANG He;QIU Jian-long;LIANG Jin-ling;JIANG Hai-jun(College of Automation&College of Artificial Intelligence,Nanjing University of Posts and Telecommunications,Nanjing Jiangsu 210023,China;School of Automation and Electrical Engineering,Linyi University,Linyi Shandong 276000,China;School of Mathematics,Southeast University,Nanjing Jiangsu 210096,China;College of Mathematics and System Science,Xinjiang University,Urumqi Xinjiang 830047,China)

机构地区：[1]南京邮电大学自动化学院人工智能学院,江苏南京210023 [2]临沂大学自动化与电气工程学院,山东临沂276000 [3]东南大学数学学院,江苏南京210096 [4]新疆大学数学与系统科学学院,新疆乌鲁木齐830047

出　　处：《控制理论与应用》2022年第8期1407-1416,共10页Control Theory & Applications

基　　金：国家自然科学基金项目(62073172,U1703262,61573194);工业控制技术国家重点实验室开放课题(ICT2022B43)资助.

摘　　要：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.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.

关 键 词：反应扩散效应 信息物理融合系统 恶意病毒 基本再生数 图灵不稳定 HOPF分岔 

分 类 号：TP309[自动化与计算机技术—计算机系统结构]