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.

Global Stability and Bifurcation Analysis of a Rumor Propagation Model with Two Discrete Delays in Social Networks

2020 ◽  
Vol 30 (12) ◽  
pp. 2050175
Author(s):  
Linhe Zhu ◽  
Xuewei Wang ◽  
Zhengdi Zhang ◽  
Shuling Shen
Keyword(s):  
Social Networks ◽  
Global Stability ◽  
Equilibrium Points ◽  
Propagation Model ◽  
Logistic Growth ◽  
Positive Equilibrium ◽  
Normal Form Theory ◽  
Center Manifold Theorem ◽  
Rumor Propagation ◽  
Discrete Delays

In this paper, we improve an Ignorant-Lurker-Spreader-Removal (ILSR) rumor propagation model as in [Yang et al., 2019] in social networks with consideration to Logistic growth and two discrete delays. First, we prove the existence of equilibrium points by calculating the basic reproduction number according to the next generation matrix. Regarding the two discrete delays as bifurcating parameters, the local asymptotical stability and Hopf bifurcation of the positive equilibrium point are discussed for six different scenarios by analyzing the characteristic equations of linearized systems. Applying the normal form theory and the center manifold theorem, some important conclusions about the stability and direction of bifurcating periodic solution are given when the two time delays are equal. Subsequently we study the global stability of the equilibrium points by constructing Lyapunov functions when the two delays disappear. Finally, we verify the conclusions through numerical simulations and perform sensitivity analysis on the basic reproduction numbers.

Dynamic Analysis of a Reaction–Diffusion Rumor Propagation Model

2016 ◽  
Vol 26 (06) ◽  
pp. 1650101 ◽  
Author(s):  
Hongyong Zhao ◽  
Linhe Zhu
Keyword(s):  
Social Networks ◽  
Time Delay ◽  
New Media ◽  
Equilibrium Point ◽  
Rapid Development ◽  
Upper And Lower Solutions ◽  
Propagation Model ◽  
Traveling Wave Solution ◽  
Rumor Spreading ◽  
Rumor Propagation

The rapid development of the Internet, especially the emergence of the social networks, leads rumor propagation into a new media era. Rumor propagation in social networks has brought new challenges to network security and social stability. This paper, based on partial differential equations (PDEs), proposes a new SIS rumor propagation model by considering the effect of the communication between the different rumor infected users on rumor propagation. The stabilities of a nonrumor equilibrium point and a rumor-spreading equilibrium point are discussed by linearization technique and the upper and lower solutions method, and the existence of a traveling wave solution is established by the cross-iteration scheme accompanied by the technique of upper and lower solutions and Schauder’s fixed point theorem. Furthermore, we add the time delay to rumor propagation and deduce the conditions of Hopf bifurcation and stability switches for the rumor-spreading equilibrium point by taking the time delay as the bifurcation parameter. Finally, numerical simulations are performed to illustrate the theoretical results.

scholarly journals Rumor Propagation Model: An Equilibrium Study

2010 ◽  
Vol 2010 ◽  
pp. 1-7 ◽  
Author(s):  
José Roberto C. Piqueira
Keyword(s):  
Initial Conditions ◽  
Equilibrium Points ◽  
Propagation Model ◽  
Epidemiological Models ◽  
Rumor Spreading ◽  
Equilibrium Study ◽  
Spreading Model ◽  
Rumor Propagation ◽  
Propagation Parameters ◽  
The 1960S

Compartmental epidemiological models have been developed since the 1920s and successfully applied to study the propagation of infectious diseases. Besides, due to their structure, in the 1960s an interesting version of these models was developed to clarify some aspects of rumor propagation, considering that spreading an infectious disease or disseminating information is analogous phenomena. Here, in an analogy with the SIR (Susceptible-Infected-Removed) epidemiological model, the ISS (Ignorant-Spreader-Stifler) rumor spreading model is studied. By using concepts from the Dynamical Systems Theory, stability of equilibrium points is established, according to propagation parameters and initial conditions. Some numerical experiments are conducted in order to validate the model.

scholarly journals A Bio-Inspired Defensive Rumor Confinement Strategy in Online Social Networks

2021 ◽  
Vol 33 (1) ◽  
pp. 47-70
Author(s):  
Santhoshkumar Srinivasan ◽  
Dhinesh Babu L. D.
Keyword(s):  
Social Networks ◽  
Online Social Networks ◽  
Propagation Model ◽  
Information Propagation ◽  
Control Approach ◽  
Rumor Propagation ◽  
Immunization Strategies ◽  
New Information ◽  
The Individual ◽  
Rumor Control

Online social networks (OSNs) are used to connect people and propagate information around the globe. Along with information propagation, rumors also penetrate across the OSNs in a massive order. Controlling the rumor propagation is utmost important to reduce the damage it causes to society. Educating the individual participants of OSNs is one of the effective ways to control the rumor faster. To educate people in OSNs, this paper proposes a defensive rumor control approach that spreads anti-rumors by the inspiration from the immunization strategies of social insects. In this approach, a new information propagation model is defined to study the defensive nature of true information against rumors. Then, an anti-rumor propagation method with a set of influential spreaders is employed to defend against the rumor. The proposed approach is compared with the existing rumor containment approaches and the results indicate that the proposed approach works well in controlling the rumors.

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 Spread Mechanism and Control Strategies of Rumor Propagation Model Considering Rumor Refutation and Information Feedback in Emergency Management

Symmetry ◽  
2021 ◽  
Vol 13 (9) ◽  
pp. 1694
Author(s):  
Jianhong Chen ◽  
Chaoqun Chen ◽  
Qinghua Song ◽  
Yifei Zhao ◽  
Longxin Deng ◽  
...  
Keyword(s):  
Equilibrium State ◽  
Emergency Management ◽  
Equilibrium Point ◽  
Open System ◽  
Endemic Equilibrium ◽  
Propagation Model ◽  
Information Feedback ◽  
Rumor Spreading ◽  
Rumor Propagation ◽  
Management Procedures

The rumor-free equilibrium state and rumor-endemic equilibrium state are two symmetric descriptions of the status of a system. The constant spreading of rumors would affect the smooth operation of emergency management procedures and cause unnecessary social and economic loss. To reduce the negative effect of rumor propagation, in this paper, we introduce a compartmental model of rumor propagation, which considers the rumor refutation of public and information feedback. By deriving mean-field equations that describe the dynamics of the model, we use analytical and numerical solutions of these equations to investigate the threshold and dynamics of the model in both the closed system and open system. The results imply that the initial equilibrium point is not stable and there exists a rumor-free equilibrium point; in the open system, there exists a threshold beyond which rumors can spread; the stability of the initial equilibrium point is related to the threshold R0 = (φ*α)/μ, and there exists a rumor-endemic equilibrium point. The development process of rumor propagation can be divided into four stages: latent period, progressive period, intense period, and recession period. Under the influence of population, rumor spreading can exceed the threshold readily because the migration rate μ is usually less than the proportion of ignorants without critical ability φ, and the rumor spreading process in an open system presents a fluctuating development, the rumor would not disappear in this autonomous system. Based on the analysis, we propose some measures, such as providing open and efficient information queries and exchange platforms, etc.

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