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Related papers: Competitive exclusion for chemostat equations with…

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In this paper, we consider a competition model between $n$ species in a chemostat including both monotone and non-monotone response functions, distinct removal rates and variable yields. We show that only the species with the lowest…

Dynamical Systems · Mathematics 2010-02-26 Tewfik Sari

A. Bornh\"oft, R. Hanke-Rauschenbach, and K. Sundmacher, [Nonlinear Dyn., 73 (2013), pp. 535-549] introduced a qualitative simplification to the ADM1 model for anaerobic digestion. We obtain global results for this model by first analyzing…

Quantitative Methods · Quantitative Biology 2019-04-15 Tyler Meadows , Marion Weedermann , Gail S. K. Wolkowicz

We give an new proof of the well-known competitive exclusion principle in the chemostat model with $n$ species competing for a single resource, for any set of increasing growth functions. The proof is constructed by induction on the number…

Classical Analysis and ODEs · Mathematics 2017-12-01 Alain Rapaport , Mario Veruete

We propose a system of differential equations modeling the competition between two obligate mutualistic species for a single nutrient in a chemostat. Each species promotes the growth of the other, and growth occurs only in the presence of…

Dynamical Systems · Mathematics 2026-03-12 Tahani Mtar , Radhouane Fekih-Salem

We study a model of competition for resource through a chemostat-type model where species consume the common resource that is constantly supplied. We assume that the species and resources are characterized by a continuous trait. As already…

Analysis of PDEs · Mathematics 2014-02-24 Sepideh Mirrahimi , Benoît Perthame , Joe Yuichiro Wakano

We study the chemostat model for one species competing for one nutrient using a Lyapunov-type analysis. We design the dilution rate function so that all solutions of the chemostat converge to a prescribed periodic solution. In terms of…

Optimization and Control · Mathematics 2007-05-23 Frederic Mazenc , Michael Malisoff , Patrick De Leenheer

A nonautonomous periodic chemostat model with delays modelling $n$ species in competition is considered. Sufficient conditions on the coefficients and consumption functions for the species are given, for both the extinction of the species…

Dynamical Systems · Mathematics 2024-03-13 Teresa Faria

This paper studies a two microbial species model in competition for a single resource in the chemostat including general interspecific density-dependent growth rates with distinct removal rates for each species. We give the necessary and…

Dynamical Systems · Mathematics 2024-01-15 Tahani Mtar , Radhouane Fekih-Salem

We investigate some chemostat models incorporating wall growth, competition, random fluctuations on the dilution rate, and different consumption functions (Monod and Haldane). We analyze the asymptotic behavior of the solutions of the…

Dynamical Systems · Mathematics 2026-03-23 Javier López-de-la-Cruz , Felipe Rivero , Carlos R. Takaessu

The classical chemostat is an intensely investigated model in ecology and bio/chemical engineering, where n-species, say $x_{1}, x_{2}...x_{n}$ compete for a single growth limiting nutrient. Classical theory predicts that depending on model…

Dynamical Systems · Mathematics 2024-06-24 Thomas Griffin , James Lathrop , Rana Parshad

We study a general chemostat model with a discrete-time delay between consumption and growth. The goal of this article is to provide sufficient and necessary conditions for persistence. This extends previous works in the matter.…

Analysis of PDEs · Mathematics 2023-06-14 Mauro Rodriguez Cartabia

We study a single-species chemostat model with variable nutrient input and variable dilution rate with delayed (fixed) response in growth. The first goal of this article is to prove that persistence implies uniform persistence. Then we…

Classical Analysis and ODEs · Mathematics 2023-01-23 Mauro Rodriguez Cartabia , Daniel Sepúlveda Oehninger

In this paper we study the stability properties of the equilibrium point for an age-structured chemostat model with renewal boundary condition and coupled substrate dynamics under constant dilution rate. This is a complex…

Dynamical Systems · Mathematics 2026-03-27 Iasson Karafyllis , Dionysios Theodosis , Miroslav Krstic

We are interested in modeling the Darwinian evolution resulting from the interplay of phenotypic variation and natural selection through ecological interactions, in the specific scales of the biological framework of adaptive dynamics.…

Probability · Mathematics 2013-02-05 Nicolas Champagnat , Pierre-Emmanuel Jabin , Sylvie Méléard

This paper is concerned with an analysis of the dynamics of a non-autonomous, single population age based growth model with harvesting formulation. First, we derive sufficient conditions for permanence and positive invariance. Then, by…

Populations and Evolution · Quantitative Biology 2020-01-10 N. S. N. V. K. Vyshnavi Devi , Debaldev Jana , M. Lakshmanan

In this paper we consider a model of a nutrient-prey-predator system in a chemostat with general functional responses, using the input concentration of nutrient as the bifurcation parameter. We study the changes in the existence of isolated…

Dynamical Systems · Mathematics 2019-11-20 Mary Ballyk , Ibrahim Jawarneh , Ross Staffeldt

We introduce two stochastic chemostat models consisting in a coupled population-nutrient process reflecting the interaction between the nutrient and the bacterias in the chemostat with finite volume. The nutrient concentration evolves…

Probability · Mathematics 2012-06-19 Pierre Collet , Servet Martinez , Sylvie Meleard , Jaime San Martin

This paper is devoted to investigate the pattern formation of a volume-filling chemotaxis model with logistic cell growth. We first apply the local stability analysis to establish sufficient conditions of destabilization for uniform…

Analysis of PDEs · Mathematics 2016-11-22 Yazhou Han , Zhongfang Li , Jicheng Tao , Manjun Ma

A competitive resource-consumer dynamical model is analyzed based on an integrated model of a competitive Lotka-Volterra model and a prey-predator Rosenzweig-MacArthur model that we call that LV-RM model throughout this paper. Resource…

Dynamical Systems · Mathematics 2023-10-26 Gholam Reza Rokni Lamouki , Mahmoud Soufbaf , Khosro Tajbakhsh

We consider a population with two equal dominated species, dynamics of which is defined by one-dimensional piecewise-continuous, two parametric functions. It is shown that for any non-zero parameters this function has two fixed points and…

Dynamical Systems · Mathematics 2019-09-17 U. A. Rozikov , J. B. Usmonov
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