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Related papers: Two-species competition model with chemotaxis: wel…

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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

Understanding the asymptotic behavior of reaction-diffusion (RD) systems is crucial for modeling processes ranging from species coexistence in ecology to biochemical interactions within cells. In this work, we analyze RD systems in which…

Dynamical Systems · Mathematics 2025-02-18 Carlos Barajas , Jean-Jacques Slotine , Domitilla Del Vecchio

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 paper we present and analyse a simple two populations model with migrations among two different environments. The populations interact by competing for resources. Equilibria are investigated. A proof for the boundedness of the…

Populations and Evolution · Quantitative Biology 2014-03-06 Davide Belocchio , Roberto Cavoretto , Giacomo Gimmelli , Alessandro Marchino , Ezio Venturino

A deterministic two-species predator-prey model with prey herd behavior is considered incorporating mutual interference and the effect of fear. We provide guidelines to the dynamical analysis of biologically feasible equilibrium points. We…

Dynamical Systems · Mathematics 2022-12-20 Kwadwo Antwi-Fordjour , Rana D. Parshad , Hannah E. Thompson , Stephanie B. Westaway

Bacteria regulate their motility through a variety of mechanisms, including quorum sensing (QS) and other density-dependent responses mediated by diffusible signals. While nonlinear density-dependent motility is well known in active-matter…

Populations and Evolution · Quantitative Biology 2026-01-21 Mattia Mattei , David Soriano-Paños , Alex Arenas

Local coexistence of species in large ecosystems is traditionally explained within the broad framework of niche theory. However, its rationale hardly justifies rich biodiversity observed in nearly homogeneous environments. Here we consider…

Populations and Evolution · Quantitative Biology 2021-11-17 Deepak Gupta , Stefano Garlaschi , Samir Suweis , Sandro Azaele , Amos Maritan

The global dynamics of the two-species Lotka-Volterra competition patch model with asymmetric dispersal is classified under the assumptions of weak competition and the weighted digraph of the connection matrix is strongly connected and…

Classical Analysis and ODEs · Mathematics 2022-01-19 Shanshan Chen , Junping Shi , Zhisheng Shuai , Yixiang Wu

We establish the global existence of weak solutions for a two-species cross-diffusion system, set on the 1-dimensional flat torus, in which the evolution of each species is governed by two mechanisms. The first of these is a diffusion which…

Analysis of PDEs · Mathematics 2025-04-28 Alpár R. Mészáros , Guy Parker

When three species compete cyclically in a well-mixed, stochastic system of $N$ individuals, extinction is known to typically occur at times scaling as the system size $N$. This happens, for example, in rock-paper-scissors games or…

Physics and Society · Physics 2019-02-20 Kevin E. Bassler , Erwin Frey , R. K. P. Zia

We prove the pathwise well-posedness of stochastic porous media and fast diffusion equations driven by nonlinear, conservative noise. As a consequence, the generation of a random dynamical system is obtained. This extends results of the…

Analysis of PDEs · Mathematics 2019-01-09 Benjamin Fehrman , Benjamin Gess

We prove short-time well-posedness and existence of global weak solutions of the Beris--Edwards model for nematic liquid crystals in the case of a bounded domain with inhomogeneous mixed Dirichlet and Neumann boundary conditions. The system…

Analysis of PDEs · Mathematics 2013-11-15 Helmut Abels , Georg Dolzmann , YuNing Liu

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

The Lotka-Volterra model reflects real ecological interactions where species compete for limited resources, potentially leading to coexistence, dominance of one species, or extinction of another. Comprehending the mechanisms governing these…

Analysis of PDEs · Mathematics 2024-10-01 Maicon Sonego , Enrique Zuazua

We study a spatially homogeneous model of a market where several agents or companies compete for a wealth resource. In analogy with ecological systems the simplest case of such models shows a kind of "competitive exclusion" principle.…

Condensed Matter · Physics 2009-11-07 Marcelo Kuperman And Horacio Wio

This paper deals with the two-species chemotaxis-competition system. About the problem, Bai--Winkler first obtained asymptotic stability under some conditions. Recently, the conditions assumed in the previous work were improved; however,…

Analysis of PDEs · Mathematics 2017-06-16 Masaaki Mizukami

We consider a mutation-selection model of a population structured by the spatial variables and a trait variable which is the diffusion rate. Competition for resource is local in spatial variables, but nonlocal in the trait variable. We…

Analysis of PDEs · Mathematics 2020-04-20 King-Yeung Lam , Yuan Lou

The entanglement of population dynamics, evolution, and adaptive radiation for species competing for resources is studied. For resource harvesting, we modify the model used in Ref. Phys. Rev. Lett. 118 048103 and introduce new resource…

Populations and Evolution · Quantitative Biology 2023-10-03 Sergei V. Koniakhin

In the present work, we investigate a model of the invasion of healthy tissue by cancer cells which is described by a system of nonlinear PDEs consisting of a cross-diffusion-reaction equation and two additional nonlinear ordinary…

Numerical Analysis · Mathematics 2023-07-18 Shahin Heydari , Petr Knobloch , Thoma Wick

In natural ecosystems, species can be characterized by the nonlinear density-dependent self-regulation of their growth profile. Species of many taxa show a substantial density-dependent reduction for low population size. Nevertheless, many…

Populations and Evolution · Quantitative Biology 2025-06-26 Amit Samadder , Arnab Chattopadhyay , Anurag Sau , Sabyasachi Bhattacharya