Search Advanced

Mathematical Biosciences and Engineering

2012, Volume 9, Issue 2: 259-279. doi: 10.3934/mbe.2012.9.259
Previous Article Next Article

Qualitative analysis of a model for co-culture of bacteria and amoebae

  • 1.
    Center for Information Technology, Bruno Kessler Foundation, via Sommarive 18, I-38123 Trento Povo
  • 2.
    Institut de Mathématiques de Bordeaux, UMR CNRS 5251 - Case 36, Université Victor Segalen Bordeaux 2, 3ter place de la Victoire 33076 Bordeaux Cedex
  • 3.
    Department of Mathematics, Shanghai Jiao Tong University, Shanghai 200240
  • Received: 01 February 2011 Accepted: 29 June 2018 Published: 01 March 2012

  • MSC : 37L10, 92D25.

  • In this article we analyze a mathematical model presented in [11]. The model consists of two scalar ordinary differential equations, which describe the interaction between bacteria and amoebae. We first give the sufficient conditions for the uniform persistence of the model, then we prove that the model can undergo Hopf bifurcation and Bogdanov-Takens bifurcation for some parameter values, respectively.

    Citation: Laura Fumanelli, Pierre Magal, Dongmei Xiao, Xiao Yu. Qualitative analysis of a model for co-culture of bacteria and amoebae[J]. Mathematical Biosciences and Engineering, 2012, 9(2): 259-279. doi: 10.3934/mbe.2012.9.259

    Related Papers:

    [1] Xiaoli Wang, Junping Shi, Guohong Zhang . Bifurcation analysis of a wild and sterile mosquito model. Mathematical Biosciences and Engineering, 2019, 16(5): 3215-3234. doi: 10.3934/mbe.2019160
    [2] Zhenliang Zhu, Yuming Chen, Zhong Li, Fengde Chen . Dynamic behaviors of a Leslie-Gower model with strong Allee effect and fear effect in prey. Mathematical Biosciences and Engineering, 2023, 20(6): 10977-10999. doi: 10.3934/mbe.2023486
    [3] Kunlun Huang, Xintian Jia, Cuiping Li . Analysis of modified Holling-Tanner model with strong Allee effect. Mathematical Biosciences and Engineering, 2023, 20(8): 15524-15543. doi: 10.3934/mbe.2023693
    [4] Mengyun Xing, Mengxin He, Zhong Li . Dynamics of a modified Leslie-Gower predator-prey model with double Allee effects. Mathematical Biosciences and Engineering, 2024, 21(1): 792-831. doi: 10.3934/mbe.2024034
    [5] Lin Chen, Xiaotian Wu, Yancong Xu, Libin Rong . Modelling the dynamics of Trypanosoma rangeli and triatomine bug with logistic growth of vector and systemic transmission. Mathematical Biosciences and Engineering, 2022, 19(8): 8452-8478. doi: 10.3934/mbe.2022393
    [6] Rongjie Yu, Hengguo Yu, Chuanjun Dai, Zengling Ma, Qi Wang, Min Zhao . Bifurcation analysis of Leslie-Gower predator-prey system with harvesting and fear effect. Mathematical Biosciences and Engineering, 2023, 20(10): 18267-18300. doi: 10.3934/mbe.2023812
    [7] Moitri Sen, Malay Banerjee, Yasuhiro Takeuchi . Influence of Allee effect in prey populations on the dynamics of two-prey-one-predator model. Mathematical Biosciences and Engineering, 2018, 15(4): 883-904. doi: 10.3934/mbe.2018040
    [8] Yingzi Liu, Zhong Li, Mengxin He . Bifurcation analysis in a Holling-Tanner predator-prey model with strong Allee effect. Mathematical Biosciences and Engineering, 2023, 20(5): 8632-8665. doi: 10.3934/mbe.2023379
    [9] Szymon Sobieszek, Matthew J. Wade, Gail S. K. Wolkowicz . Rich dynamics of a three-tiered anaerobic food-web in a chemostat with multiple substrate inflow. Mathematical Biosciences and Engineering, 2020, 17(6): 7045-7073. doi: 10.3934/mbe.2020363
    [10] Shengyu Huang, Hengguo Yu, Chuanjun Dai, Zengling Ma, Qi Wang, Min Zhao . Dynamics of a harvested cyanobacteria-fish model with modified Holling type Ⅳ functional response. Mathematical Biosciences and Engineering, 2023, 20(7): 12599-12624. doi: 10.3934/mbe.2023561
  • In this article we analyze a mathematical model presented in [11]. The model consists of two scalar ordinary differential equations, which describe the interaction between bacteria and amoebae. We first give the sufficient conditions for the uniform persistence of the model, then we prove that the model can undergo Hopf bifurcation and Bogdanov-Takens bifurcation for some parameter values, respectively.


  • Reader Comments
  • © 2012 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
通讯作者: 陈斌, bchen63@163.com
  • 1. 

    沈阳化工大学材料科学与工程学院 沈阳 110142

  1. 本站搜索
  2. 百度学术搜索
  3. 万方数据库搜索
  4. CNKI搜索
Mathematical Biosciences and Engineering
4.4

Metrics

Article views(2819) PDF downloads(523) Cited by(0)

Preview PDF
Download XML
Export Citation
Article outline
Abstract

Other Articles By Authors

Related pages

Tools

Copyright © AIMS Press

/

DownLoad:  Full-Size Img  PowerPoint
Return
Return

Catalog