Abstract: Oscillatory behavior is a ubiquitous phenomenon in various physical and biological processes. Recently, it has been reported that oscillations of wireless sensor networks infected by virus (WSNIVs) can potentially be deleterious to the security strength of systems and may even cause network congestion and paralysis. Moreover, it has been discovered that latency delays are essential for the function of WSNIVs and can drive instability and periodic oscillations, enhance complexity, and even lead to multistability and chaotic motion. However, the precise roles of such delay during the regulation process are still not completely understood. Here, the primary objective of this paper is to study oscillatory behaviors of WSNIVs with latency delay. In particular, the sufficient conditions for local stability and existence with Hopf bifurcation are obtained. Moreover, we further discuss the properties of Hopf bifurcation by using the normal form and the center manifold theorem. The obtained results show that the latency delay can drive the WSNIVs to be oscillatory even when the network is at a stable state, suggesting that such delay might be a potential hazard to the security of wireless sensor systems. Our findings highlight the importance of considering delays when developing safer and more effective wireless sensor networks. Finally, we test and analyze the above research results through numerical calculation with Matlab and simulation experiments with OPNET, and the conclusions are verified to be correct and effective in experiments.

Key words: wireless sensor networks, virus, time delay, Hopf bifurcation, LEACH