一类捕食型时滞无线传感网络蠕虫病毒传播模型  

A Delayed Predator-prey Model for Propagation of Worm in Wireless Sensor Network

作　　者：张子振[1] 丁健[2] 宋志强 ZHANG Zi-zhen;DING Jian;SONG Zhi-qiang(School of Management Science and Engineering,Anhui University of Finance and Economics,Bengbu 233030,China;School of Control Technology,Wuxi Institute of Technology,Wuxi 214121,China;School of Mechanical and Electrical Engineering,Hulunbuir University,Hulunbuir 021008,China)

机构地区：[1]安徽财经大学管理科学与工程学院,安徽蚌埠233030 [2]无锡职业技术学院控制技术学院,江苏无锡214121 [3]呼伦贝尔学院机电工程学院,内蒙古呼伦贝尔021008

出　　处：《控制工程》2021年第12期2343-2350,共8页Control Engineering of China

基　　金：国家自然科学基金资助项目(61773181,12061033)。

摘　　要：由于无线传感网络具有广泛的应用和易受恶意软件攻击的特点,其安全性问题受到了国内外研究学者的广泛关注。借助于Holling-Ⅱ类捕食模型,研究一类时滞易感-感染-重度感染-恢复-易感(susceptible-infected-terminally infected-recovered-susceptible,SITRS)无线传感网络蠕虫病毒传播模型的局部渐近稳定性和Hopf分岔。以时滞为分岔参数,利用特征值方法,得到模型局部渐近稳定和产生Hopf分岔的充分条件。然后,利用中心流形定理和规范型理论研究Hopf分岔的方向和周期解的稳定性。最后,通过仿真分析了模型的关键参数对其动力学性质的影响,仿真结果验证了理论结果的正确性。The issue of security of wireless sensor networks has drawn extensive attention of researchers at home and abroad because of their wide range of applications and vulnerability to dangerous attacks caused by malware.With the help of Holling-Ⅱ predator-prey model,the local asymptotic stability and Hopf bifurcation of a delayed susceptible-infected-terminally infected-recovered-susceptible(SITRS)wireless sensor network are investigated in this paper.Taking time delay as the bifurcation parameter and using eigenvalue method,sufficient conditions for local asymptotic stability and Hopf bifurcation are obtained.Further,the direction of Hopf bifurcation and the stability of bifurcating periodic solutions are studied by using the center manifold theorem and normal form theory.Finally,the effects of key parameters of the model on its dynamic properties are analyzed by simulation.The simulation results verify the correctness of the theoretical results.

关 键 词：无线传感网络 Holling-Ⅱ类捕食模型 稳定性 HOPF分岔 周期解 

分 类 号：O175.12[理学—数学]