具有混合隔离策略的非线性计算机病毒传播模型的Hopf分岔研究

Hopf bifurcation of nonlinear computer virus propagation model with hybrid quarantine strategy

建立了考虑潜伏期时滞和临时免疫期时滞的具有混合隔离策略的非线性计算机病毒传播模型,旨在帮助理解计算机病毒在网络中的传播规律。通过计算模型基本再生数,以不同时滞组合为分岔参数,研究了模型的局部渐近稳定性;利用中心流形定理和规范型理论分析了Hopf分岔的方向和周期解的稳定性,并通过数值模拟验证了理论分析的正确性。研究结果可为计算机病毒治理提供理论依据。

The establishment of a nonlinear computer virus propagation model with hybrid isolation strategy is helpful for understanding the propagation law of computer virus in the network. This paper proposes a new model which considers latency delay and temporary immune delay. Firstly, the basic regeneration number of the model is calculated.Then, the local asymptotic stability of the model is studied by taking the combination of different time delays as bifurcation parameters. Afterwards, the direction of Hopf bifurcation and the stability of periodic solution are calculated by using the central manifold theorem and normal form theory. The theoretical analysis is verified by numerical simulation. The research results can provide a theoretical basis for the treatment of computer virus in the future.