计算机科学 ›› 2017, Vol. 44 ›› Issue (Z6): 390-394.doi: 10.11896/j.issn.1002-137X.2017.6A.088
张晓潘,袁凌云
ZHANG Xiao-pan and YUAN Ling-yun
摘要: 研究了具有时滞扩散作用的无线传感网络病毒传播模型的振荡动力学行为。首先,在现有实验证据的基础上,通过引入时滞和扩散作用,建立了一个新的时滞偏微分方程模型,该模型能够很好地刻画无线传感网络病毒传播的现实结构。其次,将潜伏时滞作为分岔参数,通过分析正平衡点的线性化特征方程,推导出此正稳态解的稳定性以及Hopf分岔存在的充分条件。研究结果表明在潜伏时滞和扩散的共同作用下,该时滞扩散模型表现出空间均匀与空间非均匀的振荡形态,揭示了时滞和扩散作用对无线传感网络安全是有害的。最后,给出了数值模拟来验证所给理论结果的有效性。
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