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: | , , |
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| Format: | Article |
| Language: | English |
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Wiley
2019-01-01
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| Series: | Complexity |
| Online Access: | http://dx.doi.org/10.1155/2019/3492589 |
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| _version_ | 1849307875703259136 |
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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 |