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On the stability of periodic solutions in the perturbed chemostat
1. | Projet MERE INRIA-INRA, UMR Analyse des Systèmes et Biométrie INRA, 2, pl. Viala, 34060 Montpellier, France |
2. | Department of Mathematics, Louisiana State University, Baton Rouge, LA 70803-4918, United States |
3. | Department of Mathematics, University of Florida, Gainesville, FL 32611-8105, United States |
[1] |
Frederic Mazenc, Gonzalo Robledo, Michael Malisoff. Stability and robustness analysis for a multispecies chemostat model with delays in the growth rates and uncertainties. Discrete and Continuous Dynamical Systems - B, 2018, 23 (4) : 1851-1872. doi: 10.3934/dcdsb.2018098 |
[2] |
Desheng Li, P.E. Kloeden. Robustness of asymptotic stability to small time delays. Discrete and Continuous Dynamical Systems, 2005, 13 (4) : 1007-1034. doi: 10.3934/dcds.2005.13.1007 |
[3] |
Tewfik Sari, Miled El Hajji, Jérôme Harmand. The mathematical analysis of a syntrophic relationship between two microbial species in a chemostat. Mathematical Biosciences & Engineering, 2012, 9 (3) : 627-645. doi: 10.3934/mbe.2012.9.627 |
[4] |
Zhiwen Zhao. Asymptotic analysis for the electric field concentration with geometry of the core-shell structure. Communications on Pure and Applied Analysis, 2022, 21 (4) : 1109-1137. doi: 10.3934/cpaa.2022012 |
[5] |
Zhipeng Qiu, Jun Yu, Yun Zou. The asymptotic behavior of a chemostat model. Discrete and Continuous Dynamical Systems - B, 2004, 4 (3) : 721-727. doi: 10.3934/dcdsb.2004.4.721 |
[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] |
Masaaki Mizukami. Boundedness and asymptotic stability in a two-species chemotaxis-competition model with signal-dependent sensitivity. Discrete and Continuous Dynamical Systems - B, 2017, 22 (6) : 2301-2319. doi: 10.3934/dcdsb.2017097 |
[9] |
Tobias Black. Global existence and asymptotic stability in a competitive two-species chemotaxis system with two signals. Discrete and Continuous Dynamical Systems - B, 2017, 22 (4) : 1253-1272. doi: 10.3934/dcdsb.2017061 |
[10] |
Masaaki Mizukami. Improvement of conditions for asymptotic stability in a two-species chemotaxis-competition model with signal-dependent sensitivity. Discrete and Continuous Dynamical Systems - S, 2020, 13 (2) : 269-278. doi: 10.3934/dcdss.2020015 |
[11] |
Xu Pan, Liangchen Wang. Boundedness and asymptotic stability in a quasilinear two-species chemotaxis system with nonlinear signal production. Communications on Pure and Applied Analysis, 2021, 20 (6) : 2211-2236. doi: 10.3934/cpaa.2021064 |
[12] |
Yu Ma, Chunlai Mu, Shuyan Qiu. Boundedness and asymptotic stability in a two-species predator-prey chemotaxis model. Discrete and Continuous Dynamical Systems - B, 2022, 27 (7) : 4077-4095. doi: 10.3934/dcdsb.2021218 |
[13] |
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 |
[14] |
Kun Wang, Yinnian He, Yanping Lin. Long time numerical stability and asymptotic analysis for the viscoelastic Oldroyd flows. Discrete and Continuous Dynamical Systems - B, 2012, 17 (5) : 1551-1573. doi: 10.3934/dcdsb.2012.17.1551 |
[15] |
Salvatore Rionero. A nonlinear $L^2$-stability analysis for two-species population dynamics with dispersal. Mathematical Biosciences & Engineering, 2006, 3 (1) : 189-204. doi: 10.3934/mbe.2006.3.189 |
[16] |
Edoardo Beretta, Fortunata Solimano, Yanbin Tang. Analysis of a chemostat model for bacteria and virulent bacteriophage. Discrete and Continuous Dynamical Systems - B, 2002, 2 (4) : 495-520. doi: 10.3934/dcdsb.2002.2.495 |
[17] |
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 |
[18] |
Magali Tournus, Aurélie Edwards, Nicolas Seguin, Benoît Perthame. Analysis of a simplified model of the urine concentration mechanism. Networks and Heterogeneous Media, 2012, 7 (4) : 989-1018. doi: 10.3934/nhm.2012.7.989 |
[19] |
Lars Grüne, Vryan Gil Palma. Robustness of performance and stability for multistep and updated multistep MPC schemes. Discrete and Continuous Dynamical Systems, 2015, 35 (9) : 4385-4414. doi: 10.3934/dcds.2015.35.4385 |
[20] |
Xingwang Yu, Sanling Yuan. Asymptotic properties of a stochastic chemostat model with two distributed delays and nonlinear perturbation. Discrete and Continuous Dynamical Systems - B, 2020, 25 (7) : 2373-2390. doi: 10.3934/dcdsb.2020014 |
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