胡笑梅,华纯良,王有刚,张子振

• 1:安徽财经大学管理科学与工程学院

摘要(Abstract)：

研究一类具有时滞的SIRSA计算机网络病毒传播模型。以病毒的潜伏期时滞为分支参数,得到模型局部稳定和局部Hopf分支存在的充分性条件,并计算得到模型产生局部Hopf分支的时滞临界点,最后利用仿真示例验证结果的正确性。

关键词(KeyWords)： 网络病毒;时滞;Hopf分支;SIRSA模型

Abstract:

Keywords:

基金项目(Foundation): 安徽省高校优秀青年人才计划重点项目(gxyqZD2018044);; 安徽省自然科学基金项目(1608085QF145,1608085QF151)

作者(Author): 胡笑梅,华纯良,王有刚,张子振

DOI: 10.13757/j.cnki.cn34-1328/n.2018.04.004

参考文献(References)：

• [1]MISHRA B K,JHA N.Fixed period of temporary immunity after run of anti-malicious software on computer nodes[J].Applied Mathematics and Computation,2007,190(2):1207-1212.
• [2]昂蓉蓉,叶雷.带有非线性免疫率的SIRS计算机病毒传播模型[J].安庆师范学院学报(自然科学版),2016,22(3):11-14.
• [3]ZHANG C,HUANG H.Optimal control strategy for a novel computer virus propagation model on scale free networks[J].Physica A:Statistical Mechanics and Its Applications,2016,451(1):251-265.
• [4]GAN C Q.Modeling and analysis of the effect of network eigenvalue on viral spread[J].Nonlinear Dynamics,2016,84(3):1727-1733.
• [5]MUROYA Y,KUNIYA T.Global stability of nonresident computer virus models[J].Mathematical Methods in the Applied Sciences,2015,38(2):281-295.
• [6]PARSAEI M R,JAVIDAN R,KARGAR N S,et al.On the global stability of an epidemic model of computer viruses[J].Theory in Biosciences,2017,136(6):169-178.
• [7]TANG C Q,WU Y H.Global exponential stability of nonresident computer virus models[J].Nonlinear Analysis:Real World Applications,2017,34(4):149-158.
• [8]PENG Q.Analysis of a model for computer virus transmission[J].Mathematical Problems in Engineering,2015,1(1):1-11.
• [9]FENG L P,LIAO X F,HAN Q.Hopf bifurcation analysis of a delayed viral infection model in computer networks[J].Mathematical and Computer Modelling,2012,56(8):167-179.
• [10]LI X L,WEI J J.On the zeros of a fourth degree exponential polynomial with applications to a neural network model with delays[J].Chaos,Solitons and Fractals,2005,26(2):519-526.
• [11]HASSARD B D,KAZARINOFF N D,WAN Y H.Theory and applications of Hopf bifurcation[M].Cambridge:Cambridge University Press,1981:75-86.