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

2018 ◽  
Vol 2018 ◽  
pp. 1-11 ◽  
Author(s):  
Yu Yao ◽  
Qiang Fu ◽  
Wei Yang ◽  
Ying Wang ◽  
Chuan Sheng
Keyword(s):  
Time Delay ◽  
Infection Rate ◽  
Numerical Experiments ◽  
Rapid Development ◽  
Nonlinear Process ◽  
Existence Condition ◽  
Propagation Model ◽  
Positive Equilibrium ◽  
Worm Propagation ◽  
Security Issues

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.

scholarly journals Modeling and Analysis of Bifurcation in a Delayed Worm Propagation Model

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Yu Yao ◽  
Nan Zhang ◽  
Wenlong Xiang ◽  
Ge Yu ◽  
Fuxiang Gao
Keyword(s):  
Hopf Bifurcation ◽  
Time Delay ◽  
Propagation Model ◽  
Positive Equilibrium ◽  
Simulation Experiments ◽  
Death Rates ◽  
Worm Propagation ◽  
Modeling And Analysis ◽  
Internet Worm ◽  
The Stability

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 valueτ0of Hopf bifurcation is derived. The worm propagation system is locally asymptotically stable when time delay is less thanτ0. However, Hopf bifurcation appears when time delayτpasses the thresholdτ0, which means that the worm propagation system is unstable and out of control. Consequently, time delay should be adjusted to be less thanτ0to 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.

scholarly journals Bifurcation Analysis of a Delayed Worm Propagation Model with Saturated Incidence

2018 ◽  
Vol 2018 ◽  
pp. 1-9 ◽  
Author(s):  
Zizhen Zhang ◽  
Yougang Wang ◽  
Luca Guerrini
Keyword(s):  
Hopf Bifurcation ◽  
Time Delay ◽  
Sufficient Conditions ◽  
Propagation Model ◽  
Positive Equilibrium ◽  
Normal Form Theory ◽  
Worm Propagation ◽  
Center Manifold Theorem ◽  
Saturated Incidence ◽  
Parameter Values

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.

scholarly journals The Oceanographic Multipurpose Software Environment

2016 ◽  
Author(s):  
Inti Pelupessy ◽  
Ben van Werkhoven ◽  
Arjen van Elteren ◽  
Jan Viebahn ◽  
Adam Candy ◽  
...  
Keyword(s):  
Numerical Experiments ◽  
High Performance ◽  
Rapid Development ◽  
Circulation Model ◽  
Simulation Models ◽  
Ocean Model ◽  
Propagation Model ◽  
Global Ocean ◽  
Global Circulation Model ◽  
Software Environment

Abstract. In this paper we present the Oceanographic Multipurpose Software Environment (OMUSE). This framework aims to provide a homogeneous environment for existing or newly developed numerical ocean simulation codes, simplifying their use and deployment. In this way, OMUSE facilitates the design of numerical experiments that combine ocean models representing different physics or spanning different ranges of physical scales. Rapid development of simulation models is made possible through the creation of simple high-level scripts, with the low-level core part of the abstraction designed to deploy these simulations efficiently on heterogeneous high performance computing resources. Cross-verification of simulation models with different codes and numerical methods is facilitated by the unified interface that OMUSE provides. Reproducibility in numerical experiments is fostered by allowing complex numerical experiments to be expressed in portable scripts that conform to a common OMUSE interface. Here, we present the design of OMUSE as well as the modules and model components currently included, which range from a simple conceptual quasi-geostrophic solver, to the global circulation model POP. We discuss the types of the couplings that can be implemented using OMUSE and present example applications, that demonstrate the efficient and relatively straightforward model initialisation and coupling within OMUSE. These also include the concurrent use of data analysis tools on a running model. We also give examples of multi-scale and multi-physics simulations by embedding a regional ocean model into a global ocean model, and in coupling a surface wave propagation model with a coastal circulation model.

scholarly journals Analysis of a Delayed Internet Worm Propagation Model with Impulsive Quarantine Strategy

2014 ◽  
Vol 2014 ◽  
pp. 1-18 ◽  
Author(s):  
Yu Yao ◽  
Xiaodong Feng ◽  
Wei Yang ◽  
Wenlong Xiang ◽  
Fuxiang Gao
Keyword(s):  
Time Delay ◽  
Propagation Model ◽  
The Novel ◽  
Worm Propagation ◽  
Internet Worm ◽  
Internet Worms ◽  
The Stability ◽  
And Control ◽  
Theoretical Results ◽  
Significant Attention

Internet worms exploiting zero-day vulnerabilities have drawn significant attention owing to their enormous threats to Internet in the real world. To begin with, a worm propagation model with time delay in vaccination is formulated. Through theoretical analysis, it is proved that the worm propagation system is stable when the time delay is less than the thresholdτ0and Hopf bifurcation appears when time delay is equal to or greater thanτ0. Then, a worm propagation model with constant quarantine strategy is proposed. Through quantitative analysis, it is found that constant quarantine strategy has some inhibition effect but does not eliminate bifurcation. Considering all the above, we put forward impulsive quarantine strategy to eliminate worms. Theoretical results imply that the novel proposed strategy can eliminate bifurcation and control the stability of worm propagation. Finally, simulation results match numerical experiments well, which fully supports our analysis.

scholarly journals The Oceanographic Multipurpose Software Environment (OMUSE v1.0)

2017 ◽  
Vol 10 (8) ◽  
pp. 3167-3187 ◽  
Author(s):  
Inti Pelupessy ◽  
Ben van Werkhoven ◽  
Arjen van Elteren ◽  
Jan Viebahn ◽  
Adam Candy ◽  
...  
Keyword(s):  
Numerical Experiments ◽  
High Performance ◽  
Rapid Development ◽  
Circulation Model ◽  
Simulation Models ◽  
Ocean Model ◽  
Propagation Model ◽  
Global Ocean ◽  
Global Circulation Model ◽  
Software Environment

Abstract. In this paper we present the Oceanographic Multipurpose Software Environment (OMUSE). OMUSE aims to provide a homogeneous environment for existing or newly developed numerical ocean simulation codes, simplifying their use and deployment. In this way, numerical experiments that combine ocean models representing different physics or spanning different ranges of physical scales can be easily designed. Rapid development of simulation models is made possible through the creation of simple high-level scripts. The low-level core of the abstraction in OMUSE is designed to deploy these simulations efficiently on heterogeneous high-performance computing resources. Cross-verification of simulation models with different codes and numerical methods is facilitated by the unified interface that OMUSE provides. Reproducibility in numerical experiments is fostered by allowing complex numerical experiments to be expressed in portable scripts that conform to a common OMUSE interface. Here, we present the design of OMUSE as well as the modules and model components currently included, which range from a simple conceptual quasi-geostrophic solver to the global circulation model POP (Parallel Ocean Program). The uniform access to the codes' simulation state and the extensive automation of data transfer and conversion operations aids the implementation of model couplings. We discuss the types of couplings that can be implemented using OMUSE. We also present example applications that demonstrate the straightforward model initialization and the concurrent use of data analysis tools on a running model. We give examples of multiscale and multiphysics simulations by embedding a regional ocean model into a global ocean model and by coupling a surface wave propagation model with a coastal circulation model.

scholarly journals Hopf bifurcation in an Internet worm propagation model with time delay in quarantine

2013 ◽  
Vol 57 (11-12) ◽  
pp. 2635-2646 ◽  
Author(s):  
Yu Yao ◽  
Xiao-wu Xie ◽  
Hao Guo ◽  
Ge Yu ◽  
Fu-Xiang Gao ◽  
...  
Keyword(s):  
Hopf Bifurcation ◽  
Time Delay ◽  
Propagation Model ◽  
Worm Propagation ◽  
Internet Worm

Mathematical analysis of information propagation model in complex networks

2020 ◽  
Vol 34 (26) ◽  
pp. 2050240
Author(s):  
Linhe Zhu ◽  
Gui Guan ◽  
Zhengdi Zhang
Keyword(s):  
Time Delay ◽  
Online Social Networks ◽  
Nonnegative Solution ◽  
Equilibrium Points ◽  
Propagation Model ◽  
Spatial Distance ◽  
Positive Equilibrium ◽  
Rumor Spreading ◽  
Unique Existence ◽  
Rumor Propagation

In virtue of identifying the influence of nodes, the spatial distance of rumor propagation is defined with the partition and clustering in the network. Considering the temporal and spatial propagation characteristics of rumors in online social networks, we establish a delayed rumor propagation model based on the graph theory and partial functional differential equations. Firstly, the unique existence and uniform boundedness of the nonnegative solution are explored. Secondly, we discuss the existence of positive equilibrium points sufficiently. Thirdly, stabilities of the rumor-free and rumor-spreading equilibrium points are investigated according to the linearization approach and Lyapunov function. Finally, we perform several numerical simulations to validate theoretical results and show the influence of time delay on rumor propagation. Experimental results further illustrate that taking forceful actions such as increasing the time delay in the rumor-spreading process can control rumor propagation due to the timely effectiveness of the information.

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

2014 ◽  
Vol 2014 ◽  
pp. 1-13
Author(s):  
Yu Yao ◽  
Zhao Zhang ◽  
Wenlong Xiang ◽  
Wei Yang ◽  
Fuxiang Gao
Keyword(s):  
Dynamical System ◽  
Hopf Bifurcation ◽  
Time Delay ◽  
Theoretical Analysis ◽  
Time Window ◽  
Detection System ◽  
Positive Equilibrium ◽  
Worm Propagation ◽  
Local Hopf Bifurcation ◽  
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 thresholdτ0is derived. When time delay is less thanτ0, 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.

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