分数阶计算机病毒模型的稳定性与分岔分析

随着有线和无线通信网络的普及，计算机病毒已经成为当代信息社会的一大威胁，单纯依靠杀毒软件已经无法彻底清除病毒，而通过对其在互联网上的传播机制的分析，以及对其模型的研究，可以找到有效的防范计算机病毒的对策。因此，基于非线性动力学与分数阶系统理论，建立了一类具有饱和发生率的分数阶时滞SIQR计算机病毒模型。计算出模型的平衡点，并通过分析相应的特征方程研究了时滞对平衡点稳定性的影响。选择时滞作为分岔参数，得到了发生Hopf分岔的时滞临界值。研究发现，系统的动力学行为依赖于分岔的临界值，同时给出了系统局部稳定和产生Hopf分岔的条件。在此基础上，研究了分数阶阶次的变化对分岔阈值的影响。最后，通过数值模拟验证了理论分析的正确性。

Stability and Bifurcation Analysis of Fractional Order Computer Virus Model

With the popularity of wired and wireless communication networks, computer viruses have become a major threat to the contemporary information society, relying solely on antivirus software has been unable to completely eliminate viruses, and through the analysis of its transmission mechanism on the Internet, as well as the study of its model, can find effective countermeasures against computer viruses. Therefore, based on nonlinear dynamics and fractional order system theory, a class of fractional order time-delay SIQR computer virus models with saturation incidence are established. The equilibrium point of the model is calculated, and the effect of time delay on the stability of the equilibrium point is studied by analyzing the corresponding eigen equations. Selecting the time lag as the bifurcation parameter, the time delay threshold for the occurrence of Hopf bifurcation is obtained. The study found that the dynamic behavior of the system depends on the critical value of the bifurcation, and at the same time gave the conditions for the local stability of the system and the generation of Hopf bifurcation. On this basis, the effect of the change of fractional order on the bifurcation threshold is studied. Finally, the correctness of the theoretical analysis is verified by numerical simulation results.