中山大学学报自然科学版 ›› 2016, Vol. 55 ›› Issue (1): 35-38.doi: 10.13471/j.cnki.acta.snus.2016.01.006

• 研究论文 • 上一篇    下一篇

具有密度依赖和有限抗病毒能力的计算机病毒模型的前向与后向分支

李君   

  1. 西安电子科技大学数学与统计学院,陕西 西安 710071
  • 收稿日期:2015-10-16 出版日期:2016-01-25 发布日期:2016-01-25
  • 通讯作者: 李君(1981年生),男;研究方向:常微分方程及其应用;E-mail:lijun@xidian.edu.cn

Forward and backward bifurcation of a computer virus model with density-dependent and limited anti-virus ability

LI Jun   

  1. School of Mathematics and Statistics, Xidian University, Xi'an 710071, China
  • Received:2015-10-16 Online:2016-01-25 Published:2016-01-25

摘要:

研究了一个具有密度依赖和有限抗病毒能力的计算机病毒模型。首先分析了在阈值条件下系统平衡点的存在性和局部稳定性,然后给出了系统发生前向和后向分支的条件,同时证明了该系统的极限环是不存在的,并用数值模拟验证了结果。

关键词: 抗病毒能力, 稳定性, 前向分支, 后向分支

Abstract:

A computer virus model with density-dependent and limited anti-virus ability is studied. The existence of equilibria is given and the local stability is established under the threshold value condition. After some mathematical analyses, it is showed that the forward and backward bifurcations occur and alsos proved that there is no limit cycle for system. Finally, the results are confirmed by numerical simulation.

Key words: anti-virus ability, stability, forward bifurcation, backward bifurcation

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