Hopf Bifurcation Analysis of a Synthetic Drug Transmission Model with Time Delays

This paper is concerned with the Hopf bifurcation of a synthetic drug transmission model with two delays. Firstly, some sufficient conditions of delay-induced bifurcation for such a model are captured by using different combinations of the two delays as the bifurcation parameter. Secondly, based on...

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Main Authors: Zizhen Zhang, Fangfang Yang, Wanjun Xia
Format: Article
Language:English
Published: Wiley 2019-01-01
Series:Complexity
Online Access:http://dx.doi.org/10.1155/2019/3492589
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author Zizhen Zhang
Fangfang Yang
Wanjun Xia
author_facet Zizhen Zhang
Fangfang Yang
Wanjun Xia
author_sort Zizhen Zhang
collection DOAJ
description This paper is concerned with the Hopf bifurcation of a synthetic drug transmission model with two delays. Firstly, some sufficient conditions of delay-induced bifurcation for such a model are captured by using different combinations of the two delays as the bifurcation parameter. Secondly, based on the center manifold theorem and normal form theory, some sufficient conditions determining properties of the Hopf bifurcation such as the direction and the stability are established. Finally, to underline the effectiveness of the obtained results, some numerical simulations are ultimately addressed.
format Article
id doaj-art-1b9f57185f034779b16059fcc0d5e66e
institution Kabale University
issn 1076-2787
1099-0526
language English
publishDate 2019-01-01
publisher Wiley
record_format Article
series Complexity
spelling doaj-art-1b9f57185f034779b16059fcc0d5e66e2025-08-20T03:54:37ZengWileyComplexity1076-27871099-05262019-01-01201910.1155/2019/34925893492589Hopf Bifurcation Analysis of a Synthetic Drug Transmission Model with Time DelaysZizhen Zhang0Fangfang Yang1Wanjun Xia2School of Management Science and Engineering, Anhui University of Finance and Economics, Bengbu 233030, ChinaSchool of Management Science and Engineering, Anhui University of Finance and Economics, Bengbu 233030, ChinaSchool of Management Science and Engineering, Anhui University of Finance and Economics, Bengbu 233030, ChinaThis paper is concerned with the Hopf bifurcation of a synthetic drug transmission model with two delays. Firstly, some sufficient conditions of delay-induced bifurcation for such a model are captured by using different combinations of the two delays as the bifurcation parameter. Secondly, based on the center manifold theorem and normal form theory, some sufficient conditions determining properties of the Hopf bifurcation such as the direction and the stability are established. Finally, to underline the effectiveness of the obtained results, some numerical simulations are ultimately addressed.http://dx.doi.org/10.1155/2019/3492589
spellingShingle Zizhen Zhang
Fangfang Yang
Wanjun Xia
Hopf Bifurcation Analysis of a Synthetic Drug Transmission Model with Time Delays
Complexity
title Hopf Bifurcation Analysis of a Synthetic Drug Transmission Model with Time Delays
title_full Hopf Bifurcation Analysis of a Synthetic Drug Transmission Model with Time Delays
title_fullStr Hopf Bifurcation Analysis of a Synthetic Drug Transmission Model with Time Delays
title_full_unstemmed Hopf Bifurcation Analysis of a Synthetic Drug Transmission Model with Time Delays
title_short Hopf Bifurcation Analysis of a Synthetic Drug Transmission Model with Time Delays
title_sort hopf bifurcation analysis of a synthetic drug transmission model with time delays
url http://dx.doi.org/10.1155/2019/3492589
work_keys_str_mv AT zizhenzhang hopfbifurcationanalysisofasyntheticdrugtransmissionmodelwithtimedelays
AT fangfangyang hopfbifurcationanalysisofasyntheticdrugtransmissionmodelwithtimedelays
AT wanjunxia hopfbifurcationanalysisofasyntheticdrugtransmissionmodelwithtimedelays