Bifurcations and Dynamics of the Rb-E2F Pathway Involving miR449
We focused on the gene regulative network involving Rb-E2F pathway and microRNAs (miR449) and studied the influence of time delay on the dynamical behaviors of Rb-E2F pathway by using Hopf bifurcation theory. It is shown that under certain assumptions the steady state of the delay model is asymptoti...
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| Format: | Article |
| Language: | English |
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Wiley
2017-01-01
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| Series: | Complexity |
| Online Access: | http://dx.doi.org/10.1155/2017/1409865 |
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| _version_ | 1832551462517866496 |
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| author | Lingling Li Jianwei Shen |
| author_facet | Lingling Li Jianwei Shen |
| author_sort | Lingling Li |
| collection | DOAJ |
| description | We focused on the gene regulative network involving Rb-E2F pathway and microRNAs (miR449) and studied the influence of time delay on the dynamical behaviors of Rb-E2F pathway by using Hopf bifurcation theory. It is shown that under certain assumptions the steady state of the delay model is asymptotically stable for all delay values; there is a critical value under another set of conditions; the steady state is stable when the time delay is less than the critical value, while the steady state is changed to be unstable when the time delay is greater than the critical value. Thus, Hopf bifurcation appears at the steady state when the delay passes through the critical value. Numerical simulations were presented to illustrate the theoretical results. |
| format | Article |
| id | doaj-art-51a1b3136e4c43e499666e0c8076d1c0 |
| institution | Kabale University |
| issn | 1076-2787 1099-0526 |
| language | English |
| publishDate | 2017-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Complexity |
| spelling | doaj-art-51a1b3136e4c43e499666e0c8076d1c02025-02-03T06:01:25ZengWileyComplexity1076-27871099-05262017-01-01201710.1155/2017/14098651409865Bifurcations and Dynamics of the Rb-E2F Pathway Involving miR449Lingling Li0Jianwei Shen1Department of Basic Courses, Guangdong Polytechnic College, Zhaoqing 526100, ChinaInstitute of Applied Mathematics, Xuchang University, Xuchang, Henan 461000, ChinaWe focused on the gene regulative network involving Rb-E2F pathway and microRNAs (miR449) and studied the influence of time delay on the dynamical behaviors of Rb-E2F pathway by using Hopf bifurcation theory. It is shown that under certain assumptions the steady state of the delay model is asymptotically stable for all delay values; there is a critical value under another set of conditions; the steady state is stable when the time delay is less than the critical value, while the steady state is changed to be unstable when the time delay is greater than the critical value. Thus, Hopf bifurcation appears at the steady state when the delay passes through the critical value. Numerical simulations were presented to illustrate the theoretical results.http://dx.doi.org/10.1155/2017/1409865 |
| spellingShingle | Lingling Li Jianwei Shen Bifurcations and Dynamics of the Rb-E2F Pathway Involving miR449 Complexity |
| title | Bifurcations and Dynamics of the Rb-E2F Pathway Involving miR449 |
| title_full | Bifurcations and Dynamics of the Rb-E2F Pathway Involving miR449 |
| title_fullStr | Bifurcations and Dynamics of the Rb-E2F Pathway Involving miR449 |
| title_full_unstemmed | Bifurcations and Dynamics of the Rb-E2F Pathway Involving miR449 |
| title_short | Bifurcations and Dynamics of the Rb-E2F Pathway Involving miR449 |
| title_sort | bifurcations and dynamics of the rb e2f pathway involving mir449 |
| url | http://dx.doi.org/10.1155/2017/1409865 |
| work_keys_str_mv | AT linglingli bifurcationsanddynamicsoftherbe2fpathwayinvolvingmir449 AT jianweishen bifurcationsanddynamicsoftherbe2fpathwayinvolvingmir449 |