一类时滞分数阶计算机病毒模型的稳定性研究

Stability Research of a Fractional-Order Delay Computer Virus Model

本文研究一类改进的时滞分数阶计算机病毒模型正平衡点的稳定性问题.利用线性化方法和拉普拉斯变换获得模型对应的线性化系统的特征方程,通过讨论特征方程的根以及横截条件研究时滞和正平衡点稳定性之间的关系,推导了Hopf分支出现时时滞临界值的计算公式,并选择恰当的系统参数进行数值模拟以验证理论分析的合理性.

Stability of positive equilibrium point of a modified fractional-order delay computer virus model is studied in this paper.Firstly,characteristic equation of the model is obtained by using linearization method and Laplace transformation,then we theoretically explore the relationship between the delay and stability of equilibrium point basing on analysis of roots of characteristic equation and transversality condition,critical value of delay for the energence of Hopf bifurcation is achieved.Moreover,numerical simulations are made to verify the validity of the theoretical results.