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研究

Oscillatory Behaviors of Malware Propagation Model in Wireless Sensor Networks with Time Delays and Reaction-diffusion Terms

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。

This paper investigated the oscillatory behaviors in malware propagation model for wireless sensor networks with time delays and reaction-diffusion terms.First of all,based on the existing relevant experimental evidence,a new delayed functional partial differential equation model is formulated by introduction of both delay and diffusion.This model can well describe many practical architectures of malware propagation model in wireless sensor networks.Secondly,by choosing the latent delay as bifurcation parameter and analyzing the associated characteristic equation at the positive equilibrium,the stability of positive constant steady state and the sufficient condition for the existence of Hopf bifurcation are demonstrated.It is shown that the combined effects of delay and diffusion can induce the delayed diffusive model to be oscillatory,including spatially homogeneous periodic oscillations and spatially inhomogeneous periodic oscillations,suggesting that such delay and diffusion would be deleterious to the security of wireless sensor networks.Finally,numerical examples are presented to illustrate and visualize theoretical results.