一类时滞分数阶计算机病毒模型的Hopf分岔研究  

Hopf bifurcation analysis of a fractional-order delay computer virus model

作　　者：高燕鑫 石剑平[1] GAO Yan-xin;SHI Jian-ping(Department of System Science and Applied Mathematics,Kunming University of Science and Technology,Kunming 650500,China)

机构地区：[1]昆明理工大学理学院,云南昆明650500

出　　处：《陕西理工大学学报（自然科学版）》2021年第3期52-60,共9页Journal of Shaanxi University of Technology:Natural Science Edition

基　　金：国家自然科学基金资助项目(11561034);云南省教育厅科学研究基金资助项目(2017ZZX133)。

摘　　要：研究了一类时滞分数阶计算机病毒SIR模型的Hopf分岔问题。首先通过再生矩阵方法分析系统基本再生数与正平衡点之间的关系;其次以时滞作为分岔参数,利用线性化方法和Laplace变换法分析系统在正平衡点附近发生Hopf分岔的条件,并推导了时滞临界值公式;最后通过选择恰当的系统参数进行数值模拟,验证了理论分析结果的正确性,并显示了分数阶变化对系统稳定域的影响。Hopf bifurcation of a fractional-order delay computer virus model is studied.Firstly,basing on the renewable matrix method,relationship between the equilibrium point and the basic reproductive number is analyzed.Secondly,regarding the delay as a parameter,the conditions of emergence of Hopf bifurcation near the positive equilibrium point are analyzed by linearization method and Laplace transform method.Moreover,threshold formula of delay is deduced.Finally,numerical simulations are made to verify the validity of the theoretical result.Those also show the influence of fractional-order variation on the stability region of the system.

关 键 词：分数阶 时滞 正平衡点 HOPF分岔 计算机病毒模型 

分 类 号：O193[理学—数学]