Stability and Bifurcation Analysis for a Delay Differential Equation of Hepatitis B Virus Infection
The stability and bifurcation analysis for a delay differential equation of hepatitis B virus infection is investigated. We show the existence of nonnegative equilibria under some appropriated conditions. The existence of the Hopf bifurcation with delay τ at the endemic equilibria is established by...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2013/875783 |
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| _version_ | 1832557108616232960 |
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| author | Xinchao Yang Xiju Zong Xingong Cheng Zhenlai Han |
| author_facet | Xinchao Yang Xiju Zong Xingong Cheng Zhenlai Han |
| author_sort | Xinchao Yang |
| collection | DOAJ |
| description | The stability and bifurcation analysis for a delay differential equation of hepatitis B virus infection is investigated. We show the existence of nonnegative equilibria under some
appropriated conditions. The existence of the Hopf bifurcation with delay τ at the endemic equilibria is established by analyzing the distribution of the characteristic values. The explicit formulae which determine the direction of the bifurcations, stability, and the other properties of the bifurcating periodic solutions are given by using the normal form theory and the center manifold theorem. Numerical simulation verifies the theoretical results. |
| format | Article |
| id | doaj-art-7a893114d61e419193578ed18eccee0f |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-7a893114d61e419193578ed18eccee0f2025-02-03T05:43:39ZengWileyJournal of Applied Mathematics1110-757X1687-00422013-01-01201310.1155/2013/875783875783Stability and Bifurcation Analysis for a Delay Differential Equation of Hepatitis B Virus InfectionXinchao Yang0Xiju Zong1Xingong Cheng2Zhenlai Han3School of Medical and Life Science, University of Jinan, Jinan, Shandong 250022, ChinaSchool of Electrical Engineering, University of Jinan, Jinan, Shandong 250022, ChinaSchool of Electrical Engineering, University of Jinan, Jinan, Shandong 250022, ChinaSchool of Science, University of Jinan, Jinan, Shandong 250022, ChinaThe stability and bifurcation analysis for a delay differential equation of hepatitis B virus infection is investigated. We show the existence of nonnegative equilibria under some appropriated conditions. The existence of the Hopf bifurcation with delay τ at the endemic equilibria is established by analyzing the distribution of the characteristic values. The explicit formulae which determine the direction of the bifurcations, stability, and the other properties of the bifurcating periodic solutions are given by using the normal form theory and the center manifold theorem. Numerical simulation verifies the theoretical results.http://dx.doi.org/10.1155/2013/875783 |
| spellingShingle | Xinchao Yang Xiju Zong Xingong Cheng Zhenlai Han Stability and Bifurcation Analysis for a Delay Differential Equation of Hepatitis B Virus Infection Journal of Applied Mathematics |
| title | Stability and Bifurcation Analysis for a Delay Differential Equation of Hepatitis B Virus Infection |
| title_full | Stability and Bifurcation Analysis for a Delay Differential Equation of Hepatitis B Virus Infection |
| title_fullStr | Stability and Bifurcation Analysis for a Delay Differential Equation of Hepatitis B Virus Infection |
| title_full_unstemmed | Stability and Bifurcation Analysis for a Delay Differential Equation of Hepatitis B Virus Infection |
| title_short | Stability and Bifurcation Analysis for a Delay Differential Equation of Hepatitis B Virus Infection |
| title_sort | stability and bifurcation analysis for a delay differential equation of hepatitis b virus infection |
| url | http://dx.doi.org/10.1155/2013/875783 |
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