Modeling and Analysis of Bifurcation in a Delayed Worm Propagation Model

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 τ0 of Hopf bifurcation is derived. The worm propagation system is locally asymptotically stable when time delay is less than τ0. However, Hopf bifurcation appears when time delay τ passes the threshold τ0, which means that the worm propagation system is unstable and out of control. Consequently, time delay should be adjusted to be less than τ0 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

bifurcation analysis of a delayed worm propagation model with saturated incidence

This paper is concerned with a delayed SVEIR worm propagation model with saturated incidence. The main objective is to investigate the effect of the time delay on the model. Sufficient conditions for local stability of the positive equilibrium and existence of a Hopf bifurcation are obtained by choosing the time delay as the bifurcation parameter. Particularly, explicit formulas determining direction of the Hopf bifurcation and stability of the bifurcating periodic solutions are derived by using the normal form theory and the center manifold theorem. Numerical simulations for a set of parameter values are carried out to illustrate the analytical results

Stability and Hopf Bifurcation for a Delayed SLBRS Computer Virus Model

By incorporating the time delay due to the period that computers use antivirus software to clean the virus into the SLBRS model a delayed SLBRS computer virus model is proposed in this paper. The dynamical behaviors which include local stability and Hopf bifurcation are investigated by regarding the delay as bifurcating parameter. Specially, direction and stability of the Hopf bifurcation are derived by applying the normal form method and center manifold theory. Finally, an illustrative example is also presented to testify our analytical results

An information diffusion model in social networks with carrier compartment and delay

With the wide applications of the communication networks, the topic of information networks security is getting more and more attention from governments and individuals. This paper is devoted to investigating a malware propagation model with carrier compartment and delay to describe the process of malware propagation in mobile wireless sensor networks. Based on matrix theory for characteristic values, the local stability criterion of equilibrium points is established. Applying the linear approximation method of nonlinear systems, we study the existence of Hopf bifurcation at the equilibrium points. At the same time, we identify some sensitive parameters in the process of malware propagation. Finally, numerical simulations are performed to illustrate the theoretical results

An Epidemic Model of Computer Worms with Time Delay and Variable Infection Rate

With rapid development of Internet, network security issues become increasingly serious. Temporary patches have been put on the infectious hosts, which may lose efficacy on occasions. This leads to a time delay when vaccinated hosts change to susceptible hosts. On the other hand, the worm infection is usually a nonlinear process. Considering the actual situation, a variable infection rate is introduced to describe the spread process of worms. According to above aspects, we propose a time-delayed worm propagation model with variable infection rate. Then the existence condition and the stability of the positive equilibrium are derived. Due to the existence of time delay, the worm propagation system may be unstable and out of control. Moreover, the threshold τ0 of Hopf bifurcation is obtained. The worm propagation system is stable if time delay is less than τ0. When time delay is over τ0, the system will be unstable. In addition, numerical experiments have been performed, which can match the conclusions we deduce. The numerical experiments also show that there exists a threshold in the parameter a, which implies that we should choose appropriate infection rate β(t) to constrain worm prevalence. Finally, simulation experiments are carried out to prove the validity of our conclusions

Modeling and Bifurcation Research of a Worm Propagation Dynamical System with Time Delay

Both vaccination and quarantine strategy are adopted to control the Internet worm propagation. By considering the interaction infection between computers and external removable devices, a worm propagation dynamical system with time delay under quarantine strategy is constructed based on anomaly intrusion detection system (IDS). By regarding the time delay caused by time window of anomaly IDS as the bifurcation parameter, local asymptotic stability at the positive equilibrium and local Hopf bifurcation are discussed. Through theoretical analysis, a threshold τ0 is derived. When time delay is less than τ0, the worm propagation is stable and easy to predict; otherwise, Hopf bifurcation occurs so that the system is out of control and the containment strategy does not work effectively. Numerical analysis and discrete-time simulation experiments are given to illustrate the correctness of theoretical analysis