数学理论与应用 ›› 2023, Vol. 43 ›› Issue (3): 111-129.doi: 10.3969/j.issn.1006-8074.2023.03.006

• • 上一篇    

赛博攻击下韧性系统的动力学特性研究

吴怡淳1,2,闫晶晶2,3,*,丁冉2,3,唐异垒1   

  1. 1. 上海交通大学数学科学学院,上海, 200240; 2. 信息系统工程重点实验室, 南京, 210023; 3. 中国电子科技集团公司第二十八研究所, 南京, 210023
  • 出版日期:2023-09-28 发布日期:2023-10-10
  • 基金资助:
    国家自然科学基金项目(No. 11672074)资助

Research on Dynamical Properties of Resilient System under Cyber Attack

Wu Yichun1,2,Yan Jingjing2,3,*,Ding Ran2,3, Tang Yilei1   

  1. 1. School of Mathematical Sciences, Shanghai Jiao Tong University, Shanghai 200240, China; 2. Science and Technology on Information System Engineering Laboratory, Nanjing 210023, China; 3. The 28th Research Institute of CETC, Nanjing 210023, China
  • Online:2023-09-28 Published:2023-10-10

摘要:

针对提升韧性系统在复杂赛博攻击下持续保障能力的需求, 本文首先基于病毒的传播动力学原理构建赛博攻击类模型, 模拟韧性系统面临的复杂赛博威胁环境,

对其动力学特性进行深入研究; 其次, 构建一套赛博攻击下韧性系统的目标动态变化模型, 利用中心流形定理及分岔理论对韧性系统的局部稳定性进行分析;

最后, 通过Matlab 软件, 以数值和图像的方式对赛博攻击的动力学传播过程和韧性系统的目标动态变化过程进行展现.

关键词: 赛博攻击模型, 韧性系统动力学, 定性分析, 全局动力学

Abstract:

In order to improve the continuous support capability of the resilient system under complex cyber attacks, this paper first

builds a class of cyber attack model based on the principle of virus epidemical dynamics to simulate the complex cyber threat environment in the resilient system,

and deeply studies the dynamic characteristics of the model. Then, a variant target model of the resilient system under cyber attacks is constructed, and the local stability of the resilient system is analyzed by

using the center manifold theorem and the bifurcation theory.

Finally, with the Matlab software, the dynamic epidemical process of cyber attacks and the dynamic variant process of the target of the resilient system are displayed

in some numerical portraits.

Key words: Cyber attack model, Dynamics of resilient system, Qualitative analysis, Global dynamics