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We analyze purely competitive many-species Lotka-Volterra systems with random interaction matrices, focusing the attention on statistical properties of their asymptotic states. Generic features of the evolution are outlined from a…

adap-org · Physics 2009-10-30 Guillermo Abramson , Damian Zanette

We prove an existence result for a free boundary problem inspired by the modelization of accretive growth. The growth process is formulated through a level-set approach, leading to a boundary-value problem for a Hamilton-Jacobi equation…

Analysis of PDEs · Mathematics 2026-02-17 Ulisse Stefanelli

The dynamics of a local community of competing species with weak immigration from a static regional pool is studied. Implementing the generalized competitive Lotka-Volterra model with demographic noise, a rich dynamics structure with four…

Populations and Evolution · Quantitative Biology 2015-06-22 David A. Kessler , Nadav M. Shnerb

In this paper, we investigate a two-species competition model in a landscape consisting of a finite number of adjacent patches. For the two-patch scenario, by treating edge behavior at the interface as a strategy, it has been shown that…

Dynamical Systems · Mathematics 2025-12-10 Kuiyue Liu , Shanshan Chen

How do interactions between species influence their spatial distribution in an ecosystem? To answer this question, we introduce a spatially-extended ecosystem of Generalized Lotka-Volterra type, where species can diffuse and interactions…

Statistical Mechanics · Physics 2025-01-08 Alessandro Salvatore , Fabián Aguirre-López , Ruben Zakine

This paper investigates the long-time dynamics of a nonlocal epidemic model with free boundaries, where a pathogen with density $u(t,x)$ and the infected humans with density $v(t,x)$ evolve according to a reaction-diffusion system with…

Analysis of PDEs · Mathematics 2026-02-06 Yao Chen , Yihong Du , Wan-Tong Li , Rong Wang

In this note, we study the long time behavior of Lotka-Volterra systems whose coefficients vary randomly. Benam and Lobry established that randomly switching between two environments that are both favorable to the same species may lead to…

Probability · Mathematics 2016-07-18 Florent Malrieu , Tran Hoa Phu

We study the general properties of stochastic two-species models for predator-prey competition and coexistence with Lotka-Volterra type interactions defined on a $d$-dimensional lattice. Introducing spatial degrees of freedom and allowing…

Populations and Evolution · Quantitative Biology 2007-06-07 Mauro Mobilia , Ivan T. Georgiev , Uwe C. Tauber

We discuss the effects of movement and spatial heterogeneity on population dynamics via reaction-diffusion-advection models, focusing on the persistence, competition, and evolution of organisms in spatially heterogeneous environments.…

Analysis of PDEs · Mathematics 2020-07-08 King-Yeung Lam , Shuang Liu , Yuan Lou

Non-consumptive effects such as fear of depredation, can strongly influence predator-prey dynamics. These effects have not been as well studied in the case of purely competitive systems, despite ecological and social motivations for the…

Populations and Evolution · Quantitative Biology 2022-10-20 Vaibhava Srivastava , Eric M. Takyi , Rana D. Parshad

Lotka Volterra model and its modified forms have long become a major area of interest for periodic motions in nonlinear systems with competitive species. The model given by Volterra shows that its periodicity is dependent on initial…

Chaotic Dynamics · Physics 2007-05-23 Debabrata Dutta , J K Bhattacharjee

We study a chemotaxis system that includes two competitive prey and one predator species in a two-dimensional domain, where the movement of prey (resp. predators) is driven by chemicals secreted by predators (resp. prey), called mutually…

Analysis of PDEs · Mathematics 2025-08-19 Cordula Reisch , Bao-Ngoc Tran , Juan Yang

In order to understand how impulsive interventions and environmental perturbations affect dynamics of competitors, we focus on a diffusive competition model with free boundaries and periodic pulses in a temporally heterogeneous environment…

Analysis of PDEs · Mathematics 2023-09-11 Yue Meng , Zhigui Lin , Carlos Alberto Santos

Geographic ranges of communities of species evolve in response to environmental, ecological, and evolutionary forces. Understanding the effects of these forces on species' range dynamics is a major goal of spatial ecology. Previous…

Populations and Evolution · Quantitative Biology 2022-02-02 Farshad Shirani , Judith R. Miller

The dynamics of a spatially extended system of two competing species in the presence of two noise sources is studied. A correlated dichotomous noise acts on the interaction parameter and a multiplicative white noise affects directly the…

Statistical Mechanics · Physics 2009-11-11 D. Valenti , L. Schimansky-Geier , X. Sailer , B. Spagnolo

This is part two of our study on the spreading properties of the Lotka-Volterra competition-diffusion systems with a stable coexistence state. We focus on the case when the initial data are exponential decaying. By establishing a comparison…

Analysis of PDEs · Mathematics 2020-05-05 Qian Liu , Shuang Liu , King-Yeung Lam

In this note, we study the long time behavior of Lotka-Volterra systems whose coefficients vary randomly. Bena{\"i}m and Lobry (2015) recently established that randomly switching between two environments that are both favorable to the same…

Probability · Mathematics 2017-06-15 Florent Malrieu , Pierre-André Zitt

In this work, we consider the spatial-temporal multi-species competition model. A mathematical model is described by a coupled system of nonlinear diffusion-reaction equations. We use a finite volume approximation with semi-implicit time…

Numerical Analysis · Mathematics 2022-09-08 Maria Vasilyeva , Youwen Wang , Sergei Stepanov , Alexey Sadovski

In the classical Lotka-Volterra population models, the interacting species affect each other's growth rate. We propose an alternative model, in which the species affect each other through the limitation coefficients, rather then through the…

Dynamical Systems · Mathematics 2020-08-14 Philip Korman

Ecology and evolution under changing environments are important in many subfields of biology with implications for medicine. Here, we explore an example: the consequences of fluctuating environments on the emergence of antibiotic…

Populations and Evolution · Quantitative Biology 2021-04-13 Bryce Morsky , Dervis Can Vural