一类分数阶计算机病毒模型的稳定性分析  

Stability Analysis of a Fractional Order Computer Virus Model

作　　者：周学勇 路振国 程晓明 ZHOU Xueyong;LU Zhenguo;CHENG Xiaoming(College of Mathematics and Statistics,Xinyang Normal University,Xinyang 464000,China)

机构地区：[1]信阳师范学院数学与统计学院,河南信阳464000

出　　处：《信阳师范学院学报（自然科学版）》2022年第3期345-350,共6页Journal of Xinyang Normal University(Natural Science Edition)

基　　金：国家自然科学基金项目(11701495);河南省自然科学基金项目(222300420521);河南省教师教育课程改革研究项目(2022-JSJYYB-035)。

摘　　要：建立并研究了一类分数阶计算机病毒模型。讨论并证明了模型解的正性、有界性,计算得到了模型的平衡点,运用分数阶微分方程的定性与稳定性理论以及特征根方法,讨论了平衡点的局部渐近稳定性,并给出了平衡点稳定的条件。最后,通过数值模拟验证了理论分析的正确性。A class of fractional order computer virus model is established and studied.The positivity and boundedness of solutions of the model are proved and discussed,the equilibria of the model are calculated.The stability of the equilibria are discussed by using the qualitative and stability theory of fractional-order differential equations and the method of characteristic roots,then the stability conditions of the equilibria are given.Finally,the correctness of the theoretical analysis are verified by numerical simulations.

关 键 词：计算机病毒模型 分数阶 平衡点 稳定性 

分 类 号：O175.13[理学—数学]