Modeling and analysis of bifurcation in a delayed worm propagation model
type: Item
instance of: scholarly article
title: Modeling and analysis of bifurcation in a delayed worm propagation model
zbMATH Open document ID: 1397.68011
DOI: 10.1155/2013/927369
author: Yu Yao
author: Nan Zhang
author: Wenlong Xiang
author: Ge Yu
author: Fuxiang Gao
published in: Journal of Applied Mathematics
publication date: 2018-10-10T00:00:00Z
review text: Summary: 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.
Mathematics Subject Classification ID: 68M11
Mathematics Subject Classification ID: 34C60
zbMATH DE Number: 6950939
zbMATH Keywords: worm propagation
zbMATH Keywords: Hopf bifurcation
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2013/927369
OpenAlex ID: W1999648427
Wikidata QID: Q59006998
description: scientific article; zbMATH DE number 6950939