Abstract: 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.

Key words: Wireless sensor networks,Delay,Diffusion,Computer viruses