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A diffusive Lotka-Volterra competition model is considered for the combined effect of spatial dispersal and spatial variations of resource on the population persistence and exclusion. First it is shown that in a two-species system in which…

Analysis of PDEs · Mathematics 2020-07-21 Wenjie Ni , Junping Shi , Mingxin Wang

A non-autonomous discrete delayed system for a one-species chemostat based on an Ellermeyer model for the continuous case is studied. Conditions for the persistence or the extinction of the solutions are obtained respectively in terms of…

Dynamical Systems · Mathematics 2025-12-19 P. Amster , M. Rodríguez Cartabia

In this article we investigate a parabolic-parabolic-elliptic two-species chemotaxis system with weak competition and show global asymptotic stability of the coexistence steady state under a smallness condition on the chemotactic strengths,…

Analysis of PDEs · Mathematics 2016-04-13 Tobias Black , Johannes Lankeit , Masaaki Mizukami

We consider the classical chemostat model with an additional compartment connected by pure diffusion, and analyze its asymptotic properties. We investigate conditions under which this spatial structure is beneficial for species survival and…

Classical Analysis and ODEs · Mathematics 2017-11-28 María Crespo , Alain Rapaport

The current paper is concerned with the asymptotic dynamics of two species competition systems with/without chemotaxis in heterogeneous media. In the previous work \cite{ITBWS17a}, we find conditions on the parameters in such systems for…

Dynamical Systems · Mathematics 2018-08-09 Tahir Bachar Issa , Wenxian Shen

The dynamics of species' densities depend both on internal and external variables. Internal variables include frequencies of individuals exhibiting different phenotypes or living in different spatial locations. External variables include…

Populations and Evolution · Quantitative Biology 2019-03-28 Michel Benaïm , Sebastian J. Schreiber

We investigate an infection-age structured competitive epidemiological model involving multiple strains. While classical results establish competitive exclusion when a unique maximal basic reproduction number exists, we provide here a…

Analysis of PDEs · Mathematics 2026-04-01 Simon Girel , Quentin Richard

We introduce a multi-species chemotaxis type system admitting an arbitrarily large number of population species, all of which are attracted vs. repelled by a single chemical substance. The production vs. destruction rates of the chemotactic…

Analysis of PDEs · Mathematics 2017-03-07 Nikos I. Kavallaris , Tonia Ricciardi , Gabriella Zecca

If two species exhibit different nonlinear responses to a single shared resource, and if each species modifies the resource dynamics such that this favors its competitor, they may stably coexist. This coexistence mechanism, known as…

Populations and Evolution · Quantitative Biology 2015-06-16 Florian Hartig , Tamara Münkemüller , Karin Johst , Ulf Dieckmann

In this paper, we consider a two species chemotaxis system of parabolic-parabolic-elliptic type with Lotka-Volterra type competition terms in heterogeneous media. We first find various conditions on the parameters which guarantee the global…

Analysis of PDEs · Mathematics 2018-06-11 Tahir Bachar Issa , Wenxian Shen

This paper studies a chemotaxis system where cells move in response to a chemical signal within a confined habitat. The model includes external source terms that combine local and nonlocal growth with dampening effects. The main focus is on…

Analysis of PDEs · Mathematics 2025-11-11 Rafael Diaz Fuentes , Fatma Gamze Duzgun , Silvia Frassu , Giuseppe Viglialoro

We consider within-host virus models with more than one strain and allow mutation between the strains. If there is no mutation, a Lyapunov function establishes global stability of the steady state corresponding to the fittest strain. For…

Cell Behavior · Quantitative Biology 2007-08-01 Patrick De Leenheer , Sergei S. Pilyugin

This is the first of two papers where we discuss the limits imposed by competition to the biodiversity of species communities. In this first paper we study the coexistence of competing species at the fixed point of population dynamic…

Populations and Evolution · Quantitative Biology 2007-05-23 Ugo Bastolla , Michael Lässig , Susanna C. Manrubia , Angelo Valleriani

In its simplest form, the competitive exclusion principle states that a number of species competing for a smaller number of resources cannot coexist. However, it has been observed empirically that in some settings it is possible to have…

Populations and Evolution · Quantitative Biology 2021-02-18 Alexandru Hening , Dang H. Nguyen

A general system of difference equations is presented for multispecies communities with density dependent population growth and delayed maturity. Interspecific competition, mutualism, predation, commensalism, and amensalism are…

Populations and Evolution · Quantitative Biology 2025-09-03 Geoffrey R. Hosack , Maud El-Hachem , Nicholas J. Beeton

We study an one{dimensional quasilinear system proposed by J. Tello and M. Winkler [19] which models the population dynamics of two competing species attracted by the same chemical. The kinetics terms of the interacting species are chosen…

Analysis of PDEs · Mathematics 2016-11-25 Jia Hu , Qi Wang , Jingyue Yang , Lu Zhang

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

Competition between species and genotypes is a dominant factor in a variety of ecological and evolutionary processes. Biological dynamics are typically highly stochastic, and therefore, analyzing a competitive system requires accounting for…

Populations and Evolution · Quantitative Biology 2025-01-09 Ori Turkia , Nadav M. Shnerb

In this article, we study the global dynamics of a discrete two dimensional competition model. We give sufficient conditions on the persistence of one species and the existence of local asymptotically stable interior period-2 orbit for this…

Dynamical Systems · Mathematics 2011-02-14 Yun Kang , Hal Smith

We study the stochastic evolution of four species in cyclic competition in a well mixed environment. In systems composed of a finite number $N$ of particles these simple interaction rules result in a rich variety of extinction scenarios,…

Statistical Mechanics · Physics 2012-07-09 C. H. Durney , S. O. Case , M. Pleimling , R. K. P. Zia