Qualitative analysis of a model for co-culture of bacteria and amoebae
In this article we analyze a mathematical model presented in[11]. The model consists of two scalar ordinarydifferential equations, which describe the interaction betweenbacteria and amoebae. We first give the sufficient conditions for theuniform persistence of the model, then we prove that the model...
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| Format: | Article |
| Language: | English |
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AIMS Press
2012-02-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2012.9.259 |
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| author | Laura Fumanelli Pierre Magal Dongmei Xiao Xiao Yu |
| author_facet | Laura Fumanelli Pierre Magal Dongmei Xiao Xiao Yu |
| author_sort | Laura Fumanelli |
| collection | DOAJ |
| description | In this article we analyze a mathematical model presented in[11]. The model consists of two scalar ordinarydifferential equations, which describe the interaction betweenbacteria and amoebae. We first give the sufficient conditions for theuniform persistence of the model, then we prove that the model canundergo Hopf bifurcation and Bogdanov-Takens bifurcation for someparameter values, respectively. |
| format | Article |
| id | doaj-art-03b0f10e262b49df9721469569bad2ce |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2012-02-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-03b0f10e262b49df9721469569bad2ce2025-01-24T02:05:29ZengAIMS PressMathematical Biosciences and Engineering1551-00182012-02-019225927910.3934/mbe.2012.9.259Qualitative analysis of a model for co-culture of bacteria and amoebaeLaura Fumanelli0Pierre Magal1Dongmei Xiao2Xiao Yu3Center for Information Technology, Bruno Kessler Foundation, via Sommarive 18, I-38123 Trento PovoCenter for Information Technology, Bruno Kessler Foundation, via Sommarive 18, I-38123 Trento PovoCenter for Information Technology, Bruno Kessler Foundation, via Sommarive 18, I-38123 Trento PovoCenter for Information Technology, Bruno Kessler Foundation, via Sommarive 18, I-38123 Trento PovoIn this article we analyze a mathematical model presented in[11]. The model consists of two scalar ordinarydifferential equations, which describe the interaction betweenbacteria and amoebae. We first give the sufficient conditions for theuniform persistence of the model, then we prove that the model canundergo Hopf bifurcation and Bogdanov-Takens bifurcation for someparameter values, respectively.https://www.aimspress.com/article/doi/10.3934/mbe.2012.9.259bogdanov-takens bifurcationuniform persistence.hopf bifurcationpopulation dynamics |
| spellingShingle | Laura Fumanelli Pierre Magal Dongmei Xiao Xiao Yu Qualitative analysis of a model for co-culture of bacteria and amoebae Mathematical Biosciences and Engineering bogdanov-takens bifurcation uniform persistence. hopf bifurcation population dynamics |
| title | Qualitative analysis of a model for co-culture of bacteria and amoebae |
| title_full | Qualitative analysis of a model for co-culture of bacteria and amoebae |
| title_fullStr | Qualitative analysis of a model for co-culture of bacteria and amoebae |
| title_full_unstemmed | Qualitative analysis of a model for co-culture of bacteria and amoebae |
| title_short | Qualitative analysis of a model for co-culture of bacteria and amoebae |
| title_sort | qualitative analysis of a model for co culture of bacteria and amoebae |
| topic | bogdanov-takens bifurcation uniform persistence. hopf bifurcation population dynamics |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2012.9.259 |
| work_keys_str_mv | AT laurafumanelli qualitativeanalysisofamodelforcocultureofbacteriaandamoebae AT pierremagal qualitativeanalysisofamodelforcocultureofbacteriaandamoebae AT dongmeixiao qualitativeanalysisofamodelforcocultureofbacteriaandamoebae AT xiaoyu qualitativeanalysisofamodelforcocultureofbacteriaandamoebae |