Bogdanov-Takens bifurcations in the enzyme-catalyzed reaction comprising a branched network
There have been some results on bifurcations of codimension one (such as saddle-node, transcritical, pitchfork) and degenerate Hopf bifurcations for an enzyme-catalyzed reaction system comprising a branched network but no further discussion for bifurcations at its cusp. In this paper we give conditi...
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AIMS Press
2017-09-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2017078 |
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| author | Qiuyan Zhang Lingling Liu Weinian Zhang |
| author_facet | Qiuyan Zhang Lingling Liu Weinian Zhang |
| author_sort | Qiuyan Zhang |
| collection | DOAJ |
| description | There have been some results on bifurcations of codimension one (such as saddle-node, transcritical, pitchfork) and degenerate Hopf bifurcations for an enzyme-catalyzed reaction system comprising a branched network but no further discussion for bifurcations at its cusp. In this paper we give conditions for the existence of a cusp and compute the parameter curves for the Bogdanov-Takens bifurcation, which induces the appearance of homoclinic orbits and periodic orbits, indicating the tendency to steady-states or a rise of periodic oscillations for the concentrations of the substrate and the product. |
| format | Article |
| id | doaj-art-6ab41ae4bc9d4002a8152283d7a0c887 |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2017-09-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-6ab41ae4bc9d4002a8152283d7a0c8872025-01-24T02:40:31ZengAIMS PressMathematical Biosciences and Engineering1551-00182017-09-01145&61499151410.3934/mbe.2017078Bogdanov-Takens bifurcations in the enzyme-catalyzed reaction comprising a branched networkQiuyan Zhang0Lingling Liu1Weinian Zhang2Department of Mathematics, Sichuan University, Chengdu, Sichuan 610064, ChinaDepartment of Mathematics, Sichuan University, Chengdu, Sichuan 610064, ChinaDepartment of Mathematics, Sichuan University, Chengdu, Sichuan 610064, ChinaThere have been some results on bifurcations of codimension one (such as saddle-node, transcritical, pitchfork) and degenerate Hopf bifurcations for an enzyme-catalyzed reaction system comprising a branched network but no further discussion for bifurcations at its cusp. In this paper we give conditions for the existence of a cusp and compute the parameter curves for the Bogdanov-Takens bifurcation, which induces the appearance of homoclinic orbits and periodic orbits, indicating the tendency to steady-states or a rise of periodic oscillations for the concentrations of the substrate and the product.https://www.aimspress.com/article/doi/10.3934/mbe.2017078enzyme-catalyzed reactioncuspbogdanov-takens bifurcationnormal form |
| spellingShingle | Qiuyan Zhang Lingling Liu Weinian Zhang Bogdanov-Takens bifurcations in the enzyme-catalyzed reaction comprising a branched network Mathematical Biosciences and Engineering enzyme-catalyzed reaction cusp bogdanov-takens bifurcation normal form |
| title | Bogdanov-Takens bifurcations in the enzyme-catalyzed reaction comprising a branched network |
| title_full | Bogdanov-Takens bifurcations in the enzyme-catalyzed reaction comprising a branched network |
| title_fullStr | Bogdanov-Takens bifurcations in the enzyme-catalyzed reaction comprising a branched network |
| title_full_unstemmed | Bogdanov-Takens bifurcations in the enzyme-catalyzed reaction comprising a branched network |
| title_short | Bogdanov-Takens bifurcations in the enzyme-catalyzed reaction comprising a branched network |
| title_sort | bogdanov takens bifurcations in the enzyme catalyzed reaction comprising a branched network |
| topic | enzyme-catalyzed reaction cusp bogdanov-takens bifurcation normal form |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2017078 |
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