scholarly journals Local stability of Malware propagation model on network computer with two time delay

2020 ◽  
Author(s):  
Ahmadi ◽  
Widodo
2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Fangfang Yang ◽  
Zizhen Zhang

AbstractIn this manuscript, we investigate a novel Susceptible–Exposed–Infected–Quarantined–Recovered (SEIQR) COVID-19 propagation model with two delays, and we also consider supply chain transmission and hierarchical quarantine rate in this model. Firstly, we analyze the existence of an equilibrium, including a virus-free equilibrium and a virus-existence equilibrium. Then local stability and the occurrence of Hopf bifurcation have been researched by thinking of time delay as the bifurcation parameter. Besides, we calculate direction and stability of the Hopf bifurcation. Finally, we carry out some numerical simulations to prove the validity of theoretical results.


2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Zizhen Zhang ◽  
Ruibin Wei ◽  
Wanjun Xia

AbstractIn this paper, we are concerned with a delayed smoking model in which the population is divided into five classes. Sufficient conditions guaranteeing the local stability and existence of Hopf bifurcation for the model are established by taking the time delay as a bifurcation parameter and employing the Routh–Hurwitz criteria. Furthermore, direction and stability of the Hopf bifurcation are investigated by applying the center manifold theorem and normal form theory. Finally, computer simulations are implemented to support the analytic results and to analyze the effects of some parameters on the dynamical behavior of the model.


2018 ◽  
Vol 2018 ◽  
pp. 1-11 ◽  
Author(s):  
Yu Yao ◽  
Qiang Fu ◽  
Wei Yang ◽  
Ying Wang ◽  
Chuan Sheng

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.


2018 ◽  
Vol 2018 ◽  
pp. 1-19
Author(s):  
Xin-You Meng ◽  
Jiao-Guo Wang ◽  
Hai-Feng Huo

In this paper, a Holling type IV nutrient-plankton model with time delay and linear plankton harvesting is investigated. The existence and local stability of all equilibria of model without time delay are given. Regarding time delay as bifurcation parameter, such system around the interior equilibrium loses its local stability, and Hopf bifurcation occurs when time delay crosses its critical value. In addition, the properties of the bifurcating periodic solutions are investigated based on normal form theory and center manifold theorem. What is more, the global continuation of the local Hopf bifurcation is discussed by using a global Hopf bifurcation result. Furthermore, the optimal harvesting is obtained by the Pontryagin’s Maximum Principle. Finally, some numerical simulations are given to confirm our theoretical analysis.


2000 ◽  
Vol 08 (03) ◽  
pp. 255-261 ◽  
Author(s):  
DEBASIS MUKHERJEE ◽  
SANTANU RAY ◽  
DILIP KUMAR SINHA

This article concentrates on the study of delay effect of a mangrove ecosystem of detritus, detritivores and predator of detritivores. Local stability criteria are derived in the absence of delays. Conditions are found out for which the system undergoes a Hopf bifurcation. Further conditions are derived for which there can be no change in stability.


Mathematics ◽  
2021 ◽  
Vol 9 (16) ◽  
pp. 2007
Author(s):  
Guiyun Liu ◽  
Junqiang Li ◽  
Zhongwei Liang ◽  
Zhimin Peng

The traditional SIRS virus propagation model is used to analyze the malware propagation behavior of wireless rechargeable sensor networks (WRSNs) by adding a new concept: the low-energy status nodes. The SIRS-L model has been developed in this article. Furthermore, the influence of time delay during the charging behavior of the low-energy status nodes needs to be considered. Hopf bifurcation is studied by discussing the time delay that is chosen as the bifurcation parameter. Finally, the properties of the Hopf bifurcation are explored by applying the normal form theory and the center manifold theorem.


2019 ◽  
Vol 2019 ◽  
pp. 1-8 ◽  
Author(s):  
José Roberto C. Piqueira ◽  
Cristiane M. Batistela

As the beginning of the 21st century was marked by a strong development in data science and, consequently, in computer networks, models for designing preventive actions against intruding, data stealing, and destruction became mandatory. Following this line, several types of epidemiological models have been developed and improved, considering different operational approaches. The development of the research line using traditional SIR(Susceptible, Infected, Removed) model for data networks started in the 1990s. In 2005, an epidemiological compartmental model containing antidotal nodes, SIRA (Susceptible, Infected, Removed, Antidotal), was introduced to study how the antivirus policies affect the network reliability. The idea here is to study the consequence of quarantine actions in a network by modifying the SIRA model, introducing quarantine nodes generating the SIQRA (Susceptible, Infected, Quarantine, Removed, Antidotal) model. Analytical and numerical approaches result in parameter conditions for the existence and stability of disease-free and endemic equilibrium points for two different cases: saturation and nonsaturation of the quarantine population block. Based on these results, operational actions can be planned to improve the network reliability.


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