Energy constraint hinders the popularization and development of wireless sensor networks (WSNs). As an emerging technology equipped with rechargeable batteries, wireless rechargeable sensor networks (WRSNs) are being widely accepted and recognized. In this paper, we research the security issues in WRSNs which need to be addressed urgently. After considering the charging process, the activating anti-malware program process, and the launching malicious attack process in the modeling, the susceptible-infected-anti-malware-low-energy-susceptible (SIALS) model is proposed. Through the method of epidemic dynamics, this paper analyzes the local and global stabilities of the SIALS model. Besides, this paper introduces a five-tuple attack-defense game model to further study the dynamic relationship between malware and WRSNs. By introducing a cost function and constructing a Hamiltonian function, the optimal strategies for malware and WRSNs are obtained based on the Pontryagin Maximum Principle. Furthermore, the simulation results show the validation of the proposed theories and reveal the influence of parameters on the infection. In detail, the Forward-Backward Sweep method is applied to solve the issues of convergence of co-state variables at terminal moment.
Keywords: cyber security; optimal control; stability analysis; wireless rechargeable sensor network.