Discrete and data packet delays as determinants of switching stability in wireless sensor networks

Abstract

• To understand transmission dynamics of malicious signals in WSN, an energy efficient e-epidemic delay model is proposed. • Malicious signals can be controlled, system stabilizes with small delay and exhibits oscillatory behavior for large delay. • Data packet and discrete delays are responsible for stability switching and occurrence of chaotic dynamics respectively. • Occurrence of double Hopf bifurcation indicates about regular functionality and robust security of sensor network. • We examine how the stability regions and bifurcation scenario changes with the transmission rate. An attempt has been made to understand the transmission dynamics of malicious signals in wireless sensor networks . An energy efficient e-epidemic model with data packet transmission delay has been considered. Linear stability analysis is performed for all the equilibrium points, whose characteristic equations involve the time delay. Global stability and Hopf bifurcation analyses are carried out for the endemic equilibrium point of the delay system. Attention has been paid to the direction of Hopf bifurcation and the stability of the resulting periodic solutions. Numerical study exhibits double Hopf bifurcation dynamics and it causes stability switching i.e., instability to stability and back to instability or the reverse transition of the solution of the considered system. Finally, numerical simulations provide useful observations for different delays and they show an interesting bifurcation scenario. The impact of the control parameters β and τ on the system dynamics have been investigated. Our results suggest that the data packet delay and discrete delay are responsible for the stability switching and the occurrence of chaotic dynamics respectively. The presence of chaotic dynamics indicates fragile security system of the network. Looking into the simulation results, we have indicated the most effective control measures to control the propagation of malicious signals.