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Biological control of the chemostat with nonmonotonic response and different removal rates
| 1. | UMR Analyse des Systèmes et Biométrie, INRA, EPI INRA/INRIA 'MODEMIC', 2 pl. Viala 34060 Montpellier, France |
| 2. | Laboratoire de Biotechnologie de l'Environnement, INRA, Avenue des Etangs, 11100 Narbonne, France |
| [1] |
Mohamed Dellal, Bachir Bar. Global analysis of a model of competition in the chemostat with internal inhibitor. Discrete and Continuous Dynamical Systems - B, 2021, 26 (2) : 1129-1148. doi: 10.3934/dcdsb.2020156 |
| [2] |
Alain Rapaport, Mario Veruete. A new proof of the competitive exclusion principle in the chemostat. Discrete and Continuous Dynamical Systems - B, 2019, 24 (8) : 3755-3764. doi: 10.3934/dcdsb.2018314 |
| [3] |
Jianquan Li, Zuren Feng, Juan Zhang, Jie Lou. A competition model of the chemostat with an external inhibitor. Mathematical Biosciences & Engineering, 2006, 3 (1) : 111-123. doi: 10.3934/mbe.2006.3.111 |
| [4] |
H. L. Smith, X. Q. Zhao. Competitive exclusion in a discrete-time, size-structured chemostat model. Discrete and Continuous Dynamical Systems - B, 2001, 1 (2) : 183-191. doi: 10.3934/dcdsb.2001.1.183 |
| [5] |
Gonzalo Robledo. Feedback stabilization for a chemostat with delayed output. Mathematical Biosciences & Engineering, 2009, 6 (3) : 629-647. doi: 10.3934/mbe.2009.6.629 |
| [6] |
Nahla Abdellatif, Radhouane Fekih-Salem, Tewfik Sari. Competition for a single resource and coexistence of several species in the chemostat. Mathematical Biosciences & Engineering, 2016, 13 (4) : 631-652. doi: 10.3934/mbe.2016012 |
| [7] |
Hua Nie, Yuan Lou, Jianhua Wu. Competition between two similar species in the unstirred chemostat. Discrete and Continuous Dynamical Systems - B, 2016, 21 (2) : 621-639. doi: 10.3934/dcdsb.2016.21.621 |
| [8] |
Hua Nie, Feng-Bin Wang. Competition for one nutrient with recycling and allelopathy in an unstirred chemostat. Discrete and Continuous Dynamical Systems - B, 2015, 20 (7) : 2129-2155. doi: 10.3934/dcdsb.2015.20.2129 |
| [9] |
Mohamed Dellal, Bachir Bar, Mustapha Lakrib. A competition model in the chemostat with allelopathy and substrate inhibition. Discrete and Continuous Dynamical Systems - B, 2022, 27 (4) : 2025-2050. doi: 10.3934/dcdsb.2021120 |
| [10] |
Bachir Bar, Tewfik Sari. The operating diagram for a model of competition in a chemostat with an external lethal inhibitor. Discrete and Continuous Dynamical Systems - B, 2020, 25 (6) : 2093-2120. doi: 10.3934/dcdsb.2019203 |
| [11] |
Hua Nie, Sze-bi Hsu, Jianhua Wu. A competition model with dynamically allocated toxin production in the unstirred chemostat. Communications on Pure and Applied Analysis, 2017, 16 (4) : 1373-1404. doi: 10.3934/cpaa.2017066 |
| [12] |
Xiaoqing He, Sze-Bi Hsu, Feng-Bin Wang. A periodic-parabolic Droop model for two species competition in an unstirred chemostat. Discrete and Continuous Dynamical Systems, 2020, 40 (7) : 4427-4451. doi: 10.3934/dcds.2020185 |
| [13] |
Sze-Bi Hsu, Cheng-Che Li. A discrete-delayed model with plasmid-bearing, plasmid-free competition in a chemostat. Discrete and Continuous Dynamical Systems - B, 2005, 5 (3) : 699-718. doi: 10.3934/dcdsb.2005.5.699 |
| [14] |
Sergio Grillo, Jerrold E. Marsden, Sujit Nair. Lyapunov constraints and global asymptotic stabilization. Journal of Geometric Mechanics, 2011, 3 (2) : 145-196. doi: 10.3934/jgm.2011.3.145 |
| [15] |
Tewfik Sari, Frederic Mazenc. Global dynamics of the chemostat with different removal rates and variable yields. Mathematical Biosciences & Engineering, 2011, 8 (3) : 827-840. doi: 10.3934/mbe.2011.8.827 |
| [16] |
Zhiqi Lu. Global stability for a chemostat-type model with delayed nutrient recycling. Discrete and Continuous Dynamical Systems - B, 2004, 4 (3) : 663-670. doi: 10.3934/dcdsb.2004.4.663 |
| [17] |
Yifu Wang, Jingxue Yin. Global dynamics of the periodic un-stirred chemostat with a toxin-producing competitor. Communications on Pure and Applied Analysis, 2010, 9 (6) : 1639-1651. doi: 10.3934/cpaa.2010.9.1639 |
| [18] |
E. Cabral Balreira, Saber Elaydi, Rafael Luís. Local stability implies global stability for the planar Ricker competition model. Discrete and Continuous Dynamical Systems - B, 2014, 19 (2) : 323-351. doi: 10.3934/dcdsb.2014.19.323 |
| [19] |
Kuang-Hui Lin, Yuan Lou, Chih-Wen Shih, Tze-Hung Tsai. Global dynamics for two-species competition in patchy environment. Mathematical Biosciences & Engineering, 2014, 11 (4) : 947-970. doi: 10.3934/mbe.2014.11.947 |
| [20] |
Yukio Kan-On. Global bifurcation structure of stationary solutions for a Lotka-Volterra competition model. Discrete and Continuous Dynamical Systems, 2002, 8 (1) : 147-162. doi: 10.3934/dcds.2002.8.147 |
2018 Impact Factor: 1.313
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