摘要
研究一类右端不连续的计算机病毒传播模型.通过计算得到模型的基本再生数R0.运用微分包含的相关知识,给出该模型的Filippov解的定义,证明了该非连续模型的平衡点的存在唯一性.通过构造合适的Lyapunov函数,证明了当R0>1时,满足初始条件的每一个解都是在有限时间内全局收敛于地方病平衡点;当R0<1时,满足初始条件的每一个解都是在有限时间内全局收敛于无病平衡点.利用MATLAB软件进行数值模拟,验证了理论结果的正确性.
In this paper, a discontinuity on the right computer virus model was studied. The basic reproduction number R0 was obtained by calculating. With the knowledge of differential calculus, the Filippov solution for the model was defined, the existence and uniqueness of the equilibrium of the model were proved. By constructing Lyapunov function, it was proved that each solution was global convergence to the disease equilibrium in finite time when R0 〉 1, while each solution was global convergence to the free disease equilibrium in finite time when R0 〉1. Some numerical simulations were also carried out to illustrate the theoretical results with MATLAB.
出处
《杭州师范大学学报（自然科学版）》
CAS
2016年第4期408-414,444,共8页
Journal of Hangzhou Normal University(Natural Science Edition)
基金
国家自然科学基金项目(11302002)
