Citation: 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[J]. Mathematical Biosciences and Engineering, 2020, 17(6): 7045-7073. doi: 10.3934/mbe.2020363
[1] | Jinhu Xu, Yicang Zhou . Bifurcation analysis of HIV-1 infection model with cell-to-cell transmission and immune response delay. Mathematical Biosciences and Engineering, 2016, 13(2): 343-367. doi: 10.3934/mbe.2015006 |
[2] | Amer Hassan Albargi, Miled El Hajji . Mathematical analysis of a two-tiered microbial food-web model for the anaerobic digestion process. Mathematical Biosciences and Engineering, 2023, 20(4): 6591-6611. doi: 10.3934/mbe.2023283 |
[3] | Boumediene Benyahia, Tewfik Sari . Effect of a new variable integration on steady states of a two-step Anaerobic Digestion Model. Mathematical Biosciences and Engineering, 2020, 17(5): 5504-5533. doi: 10.3934/mbe.2020296 |
[4] | Xiaomeng Ma, Zhanbing Bai, Sujing Sun . Stability and bifurcation control for a fractional-order chemostat model with time delays and incommensurate orders. Mathematical Biosciences and Engineering, 2023, 20(1): 437-455. doi: 10.3934/mbe.2023020 |
[5] | Ranjit Kumar Upadhyay, Swati Mishra, Yueping Dong, Yasuhiro Takeuchi . Exploring the dynamics of a tritrophic food chain model with multiple gestation periods. Mathematical Biosciences and Engineering, 2019, 16(5): 4660-4691. doi: 10.3934/mbe.2019234 |
[6] | 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 |
[7] | Christian Cortés García, Jasmidt Vera Cuenca . Impact of alternative food on predator diet in a Leslie-Gower model with prey refuge and Holling Ⅱ functional response. Mathematical Biosciences and Engineering, 2023, 20(8): 13681-13703. doi: 10.3934/mbe.2023610 |
[8] | A. Aldurayhim, A. Elsonbaty, A. A. Elsadany . Dynamics of diffusive modified Previte-Hoffman food web model. Mathematical Biosciences and Engineering, 2020, 17(4): 4225-4256. doi: 10.3934/mbe.2020234 |
[9] | 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 |
[10] | Gunog Seo, Mark Kot . The dynamics of a simple Laissez-Faire model with two predators. Mathematical Biosciences and Engineering, 2009, 6(1): 145-172. doi: 10.3934/mbe.2009.6.145 |
[1] |
M. J. Wade, R. W. Pattinson, N. G. Parker, J. Dolfing, Emergent behaviour in a chlorophenolmineralising three-tiered microbial 'food web', J. Theor. Biol., 389 (2016), 171-186. doi: 10.1016/j.jtbi.2015.10.032
![]() |
[2] |
C. Mazur, W. Jones, C. Tebes-Stevens, H2 consumption during the microbial reductive dehalogenation of chlorinated phenols and tetrachloroethene, Biodegradation, 14 (2003), 285-295. doi: 10.1023/A:1024765706617
![]() |
[3] | L. Levén, K. Nyberg, A. Schnürer, Conversion of phenols during anaerobic digestion of organic solid waste - a review of important microorganisms and impact of temperature, J. Env. Manage., 95 (2012), 99-103. |
[4] |
T. Großkopf, O. Soyer, Microbial diversity arising from thermodynamic constraints, ISME J., 10 (2016), 2725-2733. doi: 10.1038/ismej.2016.49
![]() |
[5] |
B. Schink, Energetics of syntrophic cooperation in methanogenic degradation, Microbiol. Mol. Biol. Rev., 61 (1997), 262-280. doi: 10.1128/.61.2.262-280.1997
![]() |
[6] |
I. Bassani, P. G. Kougias, L. Treu, I. Angelidaki, Biogas upgrading via hydrogenotrophic methanogenesis in two-stage continuous stirred tank reactors at mesophilic and thermophilic conditions, Environ. Sci. Technol., 49 (2015), 12585-12593. doi: 10.1021/acs.est.5b03451
![]() |
[7] | J. Chen, M. J. Wade, J. Dolfing, O. S. Soyer, Increasing sulfate levels show a differential impact on synthetic communities comprising different methanogens and a sulfate reducer, J. Royal Soc. Interface, 16 (2019), 20190129. |
[8] |
N. W. Smith, P. R. Shorten, E. H. Altermann, N. C. Roy, W. C. McNabb, Hydrogen cross-feeders of the human gastrointestinal tract, Gut Microbes, 10 (2019), 270-288. doi: 10.1080/19490976.2018.1546522
![]() |
[9] |
T. Sari, M. J. Wade, Generalised approach to modelling a three-tiered microbial food-web, Math. Biosci., 291 (2017), 21-37. doi: 10.1016/j.mbs.2017.07.005
![]() |
[10] | M. El Hajji, N. Chorfi, M. Jleli, Mathematical modelling and analysis for a three-tiered microbial food web in a chemostat, Electron. J. Differ. Eq., 255 (2017), 1-13. |
[11] | S. Nouaoura, N. Abdellatif, R. Fekih-Salem, T. Sari, Mathematical analysis of a three-tiered model of anaerobic digestion, Preprint, hal-02540350v2. |
[12] | S. Nouaoura, R. Fekih-Salem, N. Abdellatif, T. Sari, Mathematical analysis of a three-tiered food-web in the chemostat, Preprint, hal-02878246. |
[13] | Y. Kuznestov, Elements of Applied Bifurcation Theory, Springer-Verlag, New York, 2004. |
[14] | Maple [Software]. Version 18.02. Waterloo Maple Inc., Waterloo, Ontario, 2018. Available from: https://maplesoft.com. |
[15] | MATLAB [Software]. Version 9.5.0.944444 (R2018b). The MathWorks Inc., Natick, Massachusetts, 2018. Available from: https://www.mathworks.com. |
[16] | H. L. Smith, P. Waltman, The Theory of the Chemostat: Dynamics of Microbial Competition (Cambridge Studies in Mathematical Biology), Cambridge University Press, 1995. |
[17] | G. J. Butler, H. I. Freedman, P. Waltman, Uniformly persistent systems, P. Am. Math. Soc., 96 (1986), 425-430. |
[18] | G. J. Butler, G. S. K. Wolkowicz, Predator-mediated competition in the chemostat, J. Math. Biol., 24 (1986), 167–191. |
[19] | H. R. Thieme, Convergence results and a Poincare-Bendixson trichotomy for asymptotically autonomous differential equations, J. Math. Biol., 30 (1992), 755-763. |
[20] | XPPAUT [Software]. Version 8.0. Dr. Bard Ermentrout, Dept of Mathematics, University of Pittsburgh, Pittsburgh PA, 2016. Available from: http://www.math.pitt.edu/bard/xpp/xpp.html. |
[21] | M. El Karoui, M. Hoyos-Flight, L. Fletcher, Future trends in synthetic biology—a report, Front. Bioeng. Biotechnol., 7 (2019), 175. |
[22] | H. Delattre, J. Chen, M. J. Wade, O. S. Soyer, Thermodynamic modelling of synthetic communities predicts minimum free energy requirements for sulfate reduction and methanogenesis, J. R. Soc. Interface, 17 (2020), 20200053. |
1. | Rachidi B. Salako, Wenxian Shen, Shuwen Xue, Can chemotaxis speed up or slow down the spatial spreading in parabolic–elliptic Keller–Segel systems with logistic source?, 2019, 79, 0303-6812, 1455, 10.1007/s00285-019-01400-0 | |
2. | Yingjie Zhu, Existence of a Nontrivial Steady-State Solution to a Parabolic-Parabolic Chemotaxis System with Singular Sensitivity, 2019, 2019, 1026-0226, 1, 10.1155/2019/8140380 | |
3. | Rachidi B. Salako, Wenxian Shen, Existence of traveling wave solutions of parabolic–parabolic chemotaxis systems, 2018, 42, 14681218, 93, 10.1016/j.nonrwa.2017.12.004 | |
4. |
Rachidi B. Salako, Wenxian Shen,
Parabolic–Elliptic Chemotaxis Model with Space–Time Dependent Logistic Sources on RN . III: Transition Fronts,
2020,
1040-7294,
10.1007/s10884-020-09901-z
|
|
5. | Rachidi B. Salako, Wenxian Shen, Spreading speeds and traveling waves of a parabolic-elliptic chemotaxis system with logistic source on RN, 2017, 37, 1553-5231, 6189, 10.3934/dcds.2017268 | |
6. | Yizhuo Wang, Shangjiang Guo, Dynamics for a two-species competitive Keller-Segel chemotaxis system with a free boundary, 2021, 502, 0022247X, 125259, 10.1016/j.jmaa.2021.125259 | |
7. | José Luis López, On nonstandard chemotactic dynamics with logistic growth induced by a modified complex Ginzburg–Landau equation, 2022, 148, 0022-2526, 248, 10.1111/sapm.12440 | |
8. | Yizhuo Wang, Shangjiang Guo, Traveling wave solutions for a two-species competitive Keller–Segel chemotaxis system, 2023, 73, 14681218, 103900, 10.1016/j.nonrwa.2023.103900 | |
9. | Shangbing Ai, Zengji Du, Traveling wave solutions for a Keller-Segel system with nonlinear chemical gradient, 2024, 0022247X, 129128, 10.1016/j.jmaa.2024.129128 | |
10. | Dong Li, Nengxing Tan, Xiaxia Wu, Periodic Travelling Wave Solutions in a Two-Species Chemotaxis Model with Time Delay Effect, 2025, 48, 0126-6705, 10.1007/s40840-025-01904-7 | |
11. | J. L. López, On the compatibility of a family of generalized Keller–Segel models with the Kardar–Parisi–Zhang equation: A traveling wave study, 2025, 35, 0218-2025, 1971, 10.1142/S0218202525500265 |