Access the full text.
Sign up today, get DeepDyve free for 14 days.
J. Monod, J. Bordet (1942)
Recherches sur la croissance des cultures bactériennes
S. Perdrieux, N. Thérien (1980)
Modelling the dynamics of the activated sludge wastewater treatment process in terms of the carbon variableWater Research, 14
M. Fikar, B. Chachuat, M. Latifi (2005)
Optimal operation of alternating activated sludge processesControl Engineering Practice, 13
L. Mirsky, F. Gantmacher, K. Hirsch (1961)
The Theory of MatricesThe Mathematical Gazette, 45
A. Rozich, A. Gaudy (1984)
Critical point analysis for toxic waste treatmentJournal of Environmental Engineering, 110
F. Gantmakher (1984)
The Theory of Matrices
M. Ramanathan, JR GAUDY (1971)
Steady‐state model for activated sludge with constant recycle sludge concentrationBiotechnology and Bioengineering, 13
Arun Mittal (2011)
Biological Wastewater Treatment
Liming Wang, Eduardo Sontag (2007)
Singularly Perturbed Monotone Systems and an Application to Double Phosphorylation CyclesJournal of Nonlinear Science, 18
A. Rozich, A. Goudy. (1985)
Response of phenol-acclimated activated sludge process to quantitative shock loadingJournal of Water Pollution Control Federation, 57
D. Sundstrom, H. Klei, A. Molvar (1973)
The use of dimensionless groups in the design of activated sludge reactorsWater Research, 7
JR GAUDY, Bioengineering SRINIVASARAGHAVEN, R. Dsi (1974)
Experimental studies on a kinetic model for design and operation of activated sludge processesBiotechnology and Bioengineering, 16
K Yadi (2016)
Singular perturbations on the infinite time intervalRev Afr Rech InformMath Appl, 9
G. Wolkowicz (1996)
The theory of the chemostat: Dynamics of microbial competitionBulletin of Mathematical Biology
A. Holmberg, J. Ranta (1982)
Procedures for parameter and state estimation of microbial growth process modelsAutom., 18
G. Olsson (1976)
State of the Art in Sewage Treatment Plant ControlTechnical Reports; TFRT, 7093
C. Jones (1995)
Geometric singular perturbation theory
F. Hoppensteadt (1974)
Asymptotic stability in singular perturbation problems. II: Problems having matched asymptotic expansion solutions☆Journal of Differential Equations, 15
N. Walz (1993)
Plankton Regulation Dynamics: Experiments and Models in Rotifer Continuous Cultures
Z. Fencl (1966)
CHAPTER 3 – Theoretical Analysis of Continuous Culture Systems
Karim Yadi (2008)
Singular perturbations on the infinite time intervalARIMA J., 9
(1994)
Dynamic models and expert systems for the activated sludge process
J. Hale, P. Waltman (1989)
Persistence in infinite-dimensional systemsSiam Journal on Mathematical Analysis, 20
D Herbert (1961)
A theoretical analysis of continuous culture systemsContin Cult Microorg, 12
M. Henze, W. Gujer, T. Mino, M. Loosdrecht (2015)
Activated sludge models ASM1, ASM2, ASM2d and ASM3Water intelligence online, 5
G. Robledo, F. Grognard, J. Gouzé (2012)
Global stability for a model of competition in the chemostat with microbial inputsNonlinear Analysis-real World Applications, 13
L Perko (2013)
Differential equations and dynamical systems
S. Hsu (1978)
Limiting Behavior for Competing SpeciesSiam Journal on Applied Mathematics, 34
Neil Fenichel (1979)
Geometric singular perturbation theory for ordinary differential equationsJournal of Differential Equations, 31
In this work, we study a several species aerobic chemostat model with constant recycle sludge concentration in continuous culture. We reduce the number of parameters by considering a dimensionless model. First, the existence of a global positive uniform attractor for the model with different removal rates is proved using the theory of dissipative dynamical systems. Hence, we investigate the asymptotic behavior of the model under small perturbations using methods of singular perturbation theory and we prove that, in the case of two species in competition, the unique equilibrium which is positive is globally asymptotically stable. Finally, we establish the link between the open problem of the chemostat with different removal rates and monotone functional responses, and our model when two species compete on the same nutrient. We give some numerical simulations to illustrate the results.
Acta Biotheoretica – Springer Journals
Published: May 4, 2017
Read and print from thousands of top scholarly journals.
Already have an account? Log in
Bookmark this article. You can see your Bookmarks on your DeepDyve Library.
To save an article, log in first, or sign up for a DeepDyve account if you don’t already have one.
Copy and paste the desired citation format or use the link below to download a file formatted for EndNote
Access the full text.
Sign up today, get DeepDyve free for 14 days.
All DeepDyve websites use cookies to improve your online experience. They were placed on your computer when you launched this website. You can change your cookie settings through your browser.