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网络蠕虫之间存在着复杂的关系,它们对蠕虫的传播和演化等动力学行为有着重要的影响,刻画这些关系有助于找到更好的控制和预防策略.本文建立了两类蠕虫(蠕虫I、蠕虫II)传播的数学模型,通过分析得到两个阈值条件R_1和R_2,当R_1<1和R_2<1,无病平衡点全局渐近稳定,意味着两类蠕虫最终均被清除;当R_2<11和R2>1时,存在惟一正平衡点且全局渐近稳定,即两类蠕虫(蠕虫I与蠕虫II)同时持续存在.通过理论分析可以得到要控制蠕虫病毒可以通过控制参数来实现,进一步给出控制蠕虫病毒相对应的措施.最后通过数值模拟验证了理论分析结果.
There is a complex relationship between Internet worms, which have an important influence on the dynamics of the propagation and evolution of worms, etc. It is helpful to depict these relationships to find better control and prevention strategies.Two types of worms (worm I , And worm II). Two threshold conditions R_1 and R_2 are obtained through analysis. When R_1 <1 and R_2 <1, the disease-free equilibrium is globally asymptotically stable, meaning that both types of worms are finally cleared. When R_2 <1 1 and R 2> 1), there exists a unique positive equilibrium point and the global asymptotical stability, that is, the two types of worms (worm I and worm II) persist at the same time.According to theoretical analysis, the worm can be controlled by controlling Parameters, and further give the corresponding measures to control the worm virus.Finally, numerical simulation results verify the theoretical analysis.