Search Advanced

Mathematical Biosciences and Engineering

2016, Volume 13, Issue 4: 631-652. doi: 10.3934/mbe.2016012
Previous Article Next Article

Competition for a single resource and coexistence of several species in the chemostat

  • 1.
    Université de Tunis El Manar, ENIT, LAMSIN, BP 37, Le Belvédère, 1002 Tunis
  • 2.
    IRSTEA, UMR Itap, 361 rue Jean-François Breton, 34196 Montpellier, France, and Université de Haute Alsace, LMIA, 4 rue des frères Lumière, 68093 Mulhouse
  • Received: 01 April 2015 Accepted: 29 June 2018 Published: 01 May 2016

  • MSC : 92D25, 34D20, 34D43.

  • We study a model of the chemostat with several species in competition for a single resource.We take into account the intra-specific interactions between individuals of the same population of micro-organisms andwe assume that the growth rates are increasing and the dilution rates are distinct.Using the concept of steady-state characteristics, we present a geometric characterization of the existence and stability of all equilibria.Moreover, we provide necessary and sufficient conditions on the control parameters of the system to have a positive equilibrium.Using a Lyapunov function, we give a global asymptotic stability result for the competition model of several species.The operating diagram describes the asymptotic behavior of this model with respect to control parametersand illustrates the effect of the intra-specific competition on the coexistence region of the species.

    Citation: Nahla Abdellatif, Radhouane Fekih-Salem, Tewfik Sari. Competition for a single resource and coexistence of several species in the chemostat[J]. Mathematical Biosciences and Engineering, 2016, 13(4): 631-652. doi: 10.3934/mbe.2016012

    Related Papers:

  • We study a model of the chemostat with several species in competition for a single resource.We take into account the intra-specific interactions between individuals of the same population of micro-organisms andwe assume that the growth rates are increasing and the dilution rates are distinct.Using the concept of steady-state characteristics, we present a geometric characterization of the existence and stability of all equilibria.Moreover, we provide necessary and sufficient conditions on the control parameters of the system to have a positive equilibrium.Using a Lyapunov function, we give a global asymptotic stability result for the competition model of several species.The operating diagram describes the asymptotic behavior of this model with respect to control parametersand illustrates the effect of the intra-specific competition on the coexistence region of the species.


    加载中
    [1] J. Theor. Biol., 139 (1989), 311-326.
    [2] Process Biochem., 14 (1979), 16-25.
    [3] Ph.D thesis, University of Montpellier 2 and University of Tunis el Manar, 2013. https://tel.archives-ouvertes.fr/tel-01018600.
    [4] J. Math. Anal. Appl., 397 (2013), 292-306.
    [5] ARIMA J., 14 (2011), 15-30.
    [6] AIChE J., 53 (2007), 535-539.
    [7] J. Biol. Dyn., 2 (2008), 1-13.
    [8] J. Math. Biol., 18 (1983), 255-280.
    [9] Ecol. Modell., 200 (2007), 393-402.
    [10] J. Math. Biol., 9 (1980), 115-132.
    [11] J. Math. Anal. Appl., 319 (2006), 48-60.
    [12] C. R. Biol., 329 (2006), 40-46.
    [13] Electron. J. Diff. Eqns., 125 (2007), 1-10.
    [14] C. R. Acad. Sci. Paris, Ser. I, 340 (2005), 199-204.
    [15] C. R. Biol., 329 (2006), 63-70.
    [16] Math. Biosci. Eng., 5 (2008), 539-547.
    [17] C. R. Biol., 330 (2007), 845-854.
    [18] C. R. Acad. Sci. Paris Ser. I, 348 (2010), 747-751.
    [19] Acta Appl. Math., 123 (2013), 201-219.
    [20] Math. Biosci. Eng., 8 (2011), 827-840.
    [21] Cambridge University Press, 1995.
    [22] AIChE J., 25 (1979), 863-872.
    [23] SIAM J. Appl. Math., 52 (1992), 222-233.
    [24] J. Biomath, 13 (1998), 282-291.
    [25] Differential Integral Equations, 11 (1998), 465-491.
  • Reader Comments
  • © 2016 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
2.6 3.9

Metrics

Article views(1499) PDF downloads(516) Cited by(13)

Preview PDF
Download XML
Export Citation
Article outline

Other Articles By Authors

Related pages

Tools

/

DownLoad:  Full-Size Img  PowerPoint
Return
Return

Catalog