一类具有饱和发生率的时滞恶意病毒传播模型的分岔控制策略
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南京邮电大学

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中图分类号:

O175.13;N941;O231.2

基金项目:

国家自然科学基金项目(62073172),国家自然科学基金项目(61573194),江苏省自然科学基金项目(BK20181389)


Bifurcation control strategy of malicious virus spreading model with time delays and saturated incidence rate
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Affiliation:

Nanjing University of Posts and Telecommunications

Fund Project:

The National Natural Science Foundation of China(62073172),The National Natural Science Foundation of China(61573194),The National Natural Science Foundation of Jiangsu Province(BK20181389)

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    摘要:

    本文考虑非线性的饱和发生率,建立了一种刻画信息物理融合系统中恶意病毒传播的SIRS(Susceptible-Infected-Recovered-Susceptible)模型.为了避免因Hopf分岔的产生致使恶意病毒传播扩散,本文采用参数调节法和状态反馈法相结合的混合分岔控制策略,研究信息物理融合系统的Hopf分岔控制问题,建立了受控系统的稳定性条件和分岔判据.探明了控制增益参数对Hopf分岔点和分岔极限环幅值的影响规律,并给出了分岔阈值与增益参数间的关系图.数值仿真的结果表明,本文提出的混合分岔控制策略不仅能够改变Hopf分岔点的位置,而且可以有效调节极限环幅值的大小,使得信息物理融合系统产生预期的动力学行为,有效降低恶意病毒传播的危害.

    Abstract:

    In this paper, saturated incidence rate is considered to establish a SIRS (Susceptible-Infected-Recovered-Susceptible) model characterizing the spread of malicious virus in cyber-physical systems. To avoid the spread of malicious virus due to the occurrence of Hopf bifurcation, a hybrid bifurcation controller combining the parameter adjustment method and state feedback method is designed to research the Hopf bifurcation control of the cyber-physical systems, and establish the stability conditions and bifurcation criteria of the controlled system. The influence of the control gain parameter on the Hopf bifurcation point and the amplitude of bifurcation limit cycle is explored, and the relationship between the bifurcation threshold and the gain parameter is given.The numerical simulation results show that the hybrid bifurcation control strategy proposed in this paper can not only chance the position of Hopf bifurcation point, but also greatly adjust the amplitude of the limit cycle. It makes CPS generate the the expected dynamic behaviors to effectively reduce the impact of the malicious virus spreading.

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历史
  • 收稿日期:2020-12-08
  • 最后修改日期:2021-03-16
  • 录用日期:2021-03-29
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