Bifurcations of Tumor-Immune Competition Systems with Delay
A tumor-immune competition model with delay is considered, which consists of two-dimensional nonlinear differential equation. The conditions for the linear stability of the equilibria are obtained by analyzing the distribution of eigenvalues. General formulas for the direction, period, and stability...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/723159 |
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| _version_ | 1832567090723160064 |
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| author | Ping Bi Heying Xiao |
| author_facet | Ping Bi Heying Xiao |
| author_sort | Ping Bi |
| collection | DOAJ |
| description | A tumor-immune competition model with delay is considered, which consists of two-dimensional nonlinear differential equation. The conditions for the linear stability of the equilibria are obtained by analyzing the distribution of eigenvalues. General formulas for the direction, period, and stability of the bifurcated periodic solutions are given for codimension one and codimension two bifurcations, including Hopf bifurcation, steady-state bifurcation, and B-T bifurcation. Numerical examples and simulations are given to illustrate the bifurcations analysis and obtained results. |
| format | Article |
| id | doaj-art-4578ea1f33b546d6854a8689298fe6e3 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-4578ea1f33b546d6854a8689298fe6e32025-02-03T01:02:25ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/723159723159Bifurcations of Tumor-Immune Competition Systems with DelayPing Bi0Heying Xiao1Department of Mathematics, Shanghai Key Laboratory of PMMP, East China Normal University, 500 Dongchuan Road, Shanghai 200241, ChinaDepartment of Mathematics, Shanghai Key Laboratory of PMMP, East China Normal University, 500 Dongchuan Road, Shanghai 200241, ChinaA tumor-immune competition model with delay is considered, which consists of two-dimensional nonlinear differential equation. The conditions for the linear stability of the equilibria are obtained by analyzing the distribution of eigenvalues. General formulas for the direction, period, and stability of the bifurcated periodic solutions are given for codimension one and codimension two bifurcations, including Hopf bifurcation, steady-state bifurcation, and B-T bifurcation. Numerical examples and simulations are given to illustrate the bifurcations analysis and obtained results.http://dx.doi.org/10.1155/2014/723159 |
| spellingShingle | Ping Bi Heying Xiao Bifurcations of Tumor-Immune Competition Systems with Delay Abstract and Applied Analysis |
| title | Bifurcations of Tumor-Immune Competition Systems with Delay |
| title_full | Bifurcations of Tumor-Immune Competition Systems with Delay |
| title_fullStr | Bifurcations of Tumor-Immune Competition Systems with Delay |
| title_full_unstemmed | Bifurcations of Tumor-Immune Competition Systems with Delay |
| title_short | Bifurcations of Tumor-Immune Competition Systems with Delay |
| title_sort | bifurcations of tumor immune competition systems with delay |
| url | http://dx.doi.org/10.1155/2014/723159 |
| work_keys_str_mv | AT pingbi bifurcationsoftumorimmunecompetitionsystemswithdelay AT heyingxiao bifurcationsoftumorimmunecompetitionsystemswithdelay |