Modeling and Analysis of Bifurcation in a Delayed Worm Propagation Model

Abstract

A delayed worm propagation model with birth and death rates is formulated. The stability of the positive equilibrium is studied. Through theoretical analysis, a critical value ${\tau }_0$ of Hopf bifurcation is derived. The worm propagation system is locally asymptotically stable when time delay is less than ${\tau }_0$. However, Hopf bifurcation appears when time delay $\tau$ passes the threshold ${\tau }_0$, which means that the worm propagation system is unstable and out of control. Consequently, time delay should be adjusted to be less than ${\tau }_0$ to ensure the stability of the system stable and better prediction of the scale and speed of Internet worm spreading. Finally, numerical and simulation experiments are presented to simulate the system, which fully support our analysis.