信息物理融合系统中恶意软件传播动力学研究
The Spreading Dynamics of Malicious Softwares in Cyber？？Physical System

针对恶意软件在信息物理融合系统(cyber？？physical system, CPS)中的传播机理难以描述的问题,提出了一种自适应SIQRS(susceptible？？infected？？quarantined？？recovered？？susceptible)传播动力学模型。该模型采用节点隔离机制描述CPS的感知和控制能力,引入链路重连机制刻画CPS的自适应性,进一步分析了恶意软件在CPS中的传播规则,并依据平均场理论建立了相应的微分动力学方程。不同参数条件下的仿真结果表明:当感染率小于存在阈值时,恶意软件无法在CPS内传播;当感染率大于存在阈值且小于传播阈值时,CPS发生滞后分岔并出现双稳态现象;当感染率大于传播阈值时,CPS稳定在地方病平衡状态;当参数满足特定条件时,CPS会发生Hopf分岔。研究表明,所提模型能够准确刻画恶意软件在CPS中的传播机理。
An adaptive SIQRS(susceptible？？infected？？quarantined？？recovered？？susceptible) spreading dynamics model is proposed to solve the problem that it is difficult to describe the spreading mechanism of malicious softwares in cyber？？physical system (CPS). The quarantined mechanism is employed to describe the perception and control abilities of CPS, and the link rewired mechanism is introduced to depict the adaptability of CPS. The spreading rules of malicious softwares are analyzed, and their differential dynamic equations are presented based on the mean field theory. Numerical simulation results with different parameters show that when the infection rate is less than the epidemic persistence threshold, malicious softwares cannot spread in CPS; when the infection rate is larger than the epidemic persistence threshold and less than the epidemic threshold, a backward bifurcation occurs which causes the bistability; when the infection rate is larger than the epidemic threshold, CPS is stable at the endemic equilibrium; and a Hopf bifurcation occurs when the parameters satisfy a specific condition. It is concluded that the adaptive SIQRS model can accurately describe the spreading mechanism of malicious softwares in CPS