Bifurcation analysis of an e-SEIARS model with multiple delays for point-to-group worm propagation
Abstract In this paper, by taking two important network environment factors (namely point-to-group worm propagation and benign worms) into consideration, a mathematical model with multiple delays to model the worm prevalence is presented. Sufficient conditions for the local stability of the unique e...
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Online Access: | http://link.springer.com/article/10.1186/s13662-019-2164-7 |
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doaj-7c91050b6208452c98f9e1acc8cd0e6e2020-11-25T03:37:41ZengSpringerOpenAdvances in Difference Equations1687-18472019-06-012019112610.1186/s13662-019-2164-7Bifurcation analysis of an e-SEIARS model with multiple delays for point-to-group worm propagationZizhen Zhang0Tao Zhao1School of Management Science and Engineering, Anhui University of Finance and EconomicsSchool of Management Science and Engineering, Anhui University of Finance and EconomicsAbstract In this paper, by taking two important network environment factors (namely point-to-group worm propagation and benign worms) into consideration, a mathematical model with multiple delays to model the worm prevalence is presented. Sufficient conditions for the local stability of the unique endemic equilibrium and the existence of a Hopf bifurcation are demonstrated by choosing the different combinations of the three delays and analyzing the associated characteristic equation. Directly afterward, the stability and direction of the bifurcated periodic solutions are investigated by using center manifold theorem and the normal form theory. Finally, special attention is paid to some numerical simulations in order to verify the obtained theoretical results.http://link.springer.com/article/10.1186/s13662-019-2164-7DelaysHopf bifurcationStabilityPoint-to-group propagationPeriodic solutions |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Zizhen Zhang Tao Zhao |
spellingShingle |
Zizhen Zhang Tao Zhao Bifurcation analysis of an e-SEIARS model with multiple delays for point-to-group worm propagation Advances in Difference Equations Delays Hopf bifurcation Stability Point-to-group propagation Periodic solutions |
author_facet |
Zizhen Zhang Tao Zhao |
author_sort |
Zizhen Zhang |
title |
Bifurcation analysis of an e-SEIARS model with multiple delays for point-to-group worm propagation |
title_short |
Bifurcation analysis of an e-SEIARS model with multiple delays for point-to-group worm propagation |
title_full |
Bifurcation analysis of an e-SEIARS model with multiple delays for point-to-group worm propagation |
title_fullStr |
Bifurcation analysis of an e-SEIARS model with multiple delays for point-to-group worm propagation |
title_full_unstemmed |
Bifurcation analysis of an e-SEIARS model with multiple delays for point-to-group worm propagation |
title_sort |
bifurcation analysis of an e-seiars model with multiple delays for point-to-group worm propagation |
publisher |
SpringerOpen |
series |
Advances in Difference Equations |
issn |
1687-1847 |
publishDate |
2019-06-01 |
description |
Abstract In this paper, by taking two important network environment factors (namely point-to-group worm propagation and benign worms) into consideration, a mathematical model with multiple delays to model the worm prevalence is presented. Sufficient conditions for the local stability of the unique endemic equilibrium and the existence of a Hopf bifurcation are demonstrated by choosing the different combinations of the three delays and analyzing the associated characteristic equation. Directly afterward, the stability and direction of the bifurcated periodic solutions are investigated by using center manifold theorem and the normal form theory. Finally, special attention is paid to some numerical simulations in order to verify the obtained theoretical results. |
topic |
Delays Hopf bifurcation Stability Point-to-group propagation Periodic solutions |
url |
http://link.springer.com/article/10.1186/s13662-019-2164-7 |
work_keys_str_mv |
AT zizhenzhang bifurcationanalysisofaneseiarsmodelwithmultipledelaysforpointtogroupwormpropagation AT taozhao bifurcationanalysisofaneseiarsmodelwithmultipledelaysforpointtogroupwormpropagation |
_version_ |
1724544507234484224 |