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首页> 外文期刊>International Journal of Modern Physics, B. Condensed Matter Physics, Statistical Physics, Applied Physics >Global stability and Hopf bifurcation of a delayed computer virus propagation model with saturation incidence rate and temporary immunity
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Global stability and Hopf bifurcation of a delayed computer virus propagation model with saturation incidence rate and temporary immunity

机译：具有饱和发生率和暂时免疫性的延迟计算机病毒传播模型的全局稳定性和Hopf分支

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摘要

In this paper, a delayed computer virus propagation model with a saturation incidence rate and a time delay describing temporary immune period is proposed and its dynamical behaviors are studied. The threshold value No is given to determine whether the virus dies out completely. By comparison arguments and iteration technique, sufficient conditions are obtained for the global asymptotic stabilities of the virus-free equilibrium and the virus equilibrium. Taking the delay as a parameter, local Hopf bifurcations are demonstrated. Furthermore, the direction of Hopf bifurcation and the stabilities of the bifurcating periodic solutions are determined by the normal form theory and the center manifold theorem for functional differential equations (FDEs). Finally, numerical simulations are carried out to illustrate the main theoretical results.
机译：本文提出了一种具有饱和发生率和时延的计算机病毒传播延迟模型，该模型描述了暂时的免疫周期，并研究了其动力学行为。给出阈值No以确定病毒是否完全消失。通过比较论证和迭代技术，获得了无病毒平衡和病毒平衡的全局渐近稳定性的充分条件。以时延为参数，证明了局部Hopf分支。此外，霍普夫分支的方向和分支周期解的稳定性由泛函形式方程和泛函微分方程的中心流形定理确定。最后，进行了数值模拟以说明主要的理论结果。

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