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This paper is concerned with the classical two-species Lotka-Volterra diffusion system with strong competition. The sharp dynamical behavior of the solution is established in two different situations: either one species is an invasive one…

Analysis of PDEs · Mathematics 2020-07-14 Rui Peng , Chang-Hong Wu , Maolin Zhou

We consider a spatial multi-type branching model in which individuals migrate in geographic space according to random walks and reproduce according to a state-dependent branching mechanism which can be sub-, super- or critical depending on…

Probability · Mathematics 2015-09-15 Andreas Greven , Anja Sturm , Anita Winter , Iljana Zähle

In this article we investigate two free boundary problems for a Lotka-Volterra competition system in a higher space dimension with sign-changing coefficients. One may be viewed as describing how two competing species invade if they occupy…

Analysis of PDEs · Mathematics 2015-04-13 Yonggang Zhao , Mingxin Wang

In this paper, we study three two competing species Lotka-Volterra competition models on finite connected graphs, with Dirichlet, Neumann or no boundary conditions. We get that when time goes to infinity, either one specie extincts while…

Analysis of PDEs · Mathematics 2022-10-26 Yuanyang Hu , Chengxia Lei

In this paper, we are concerned with the permanence of a Lotka-Volterra model of three competing species with seasonal succession. Based on the existence of a carrying simplex, that is a globally attracting hypersurface of codimension one,…

Dynamical Systems · Mathematics 2024-03-01 Lei Niu , Xizhuang Xie

We analyze a general theory for coexistence and extinction of ecological communities that are influenced by stochastic temporal environmental fluctuations. The results apply to discrete time (stochastic difference equations), continuous…

Populations and Evolution · Quantitative Biology 2021-05-19 Alexandru Hening , Dang H. Nguyen , Peter Chesson

This paper studies the Lotka-Volterra competition model with cross-diffusion terms under homogeneous Dirichlet boundary conditions. We consider the asymptotic behavior of positive steady-states as equal two cross-diffusion coefficients tend…

Analysis of PDEs · Mathematics 2023-02-14 Jumpei Inoue , Kousuke Kuto , Homare Sato

In this paper we study the long term dynamics of two prey species and one predator species. In the deterministic setting, if we assume the interactions are of Lotka-Volterra type (competition or predation), the long term behavior of this…

Probability · Mathematics 2021-11-29 Alexandru Hening , Dang Nguyen , Nhu Nguyen , Harrison Watts

We investigate the controllability of the competition-diffusion Lotka-Volterra system. Our primary focus is on the one-dimensional setting with Dirichlet boundary controls, interpreted as ecological management policies regulating the…

Analysis of PDEs · Mathematics 2025-08-04 Elisa Affili , Enrique Zuazua

The symbiotic branching model describes the dynamics of a spatial two-type population, where locally particles branch at a rate given by the frequency of the other type combined with nearest-neighbour migration. This model generalizes…

Probability · Mathematics 2021-07-01 Jochen Blath , Marcel Ortgiese

In the framework of Lotka-Volterra dynamics with evolutionary parameter variation, it is shown that a system of two competing species which is evolutionarily unstable, if left to themselves, is stabilized by a commmon predator preying on…

Condensed Matter · Physics 2009-11-10 Taksu Cheon , Shigemi Ohta

We consider two dimensional Lotka-Volterra systems in fluctuating environment. Relying on recent results on stochastic persistence and piecewise deterministic Markov processes, we show that random switching between two environments both…

Probability · Mathematics 2016-12-16 Michel Benaïm , Claude Lobry

If one isolated species is supposed to evolve following the logistic mapping, then we are tempted to think that the dynamics of two species can be expressed by a coupled system of two discrete logistic equations. As three basic…

Adaptation and Self-Organizing Systems · Physics 2007-05-23 R. Lopez-Ruiz , D. Fournier-Prunaret

In this work, we consider a system of differential equations modeling the dynamics of some populations of preys and predators, moving in space according to rapidly oscillating time-dependent transport terms, and interacting with each other…

Analysis of PDEs · Mathematics 2015-12-08 Francois Castella , Philippe Chartier , Julie Sauzeau

We consider a couple of models for the dynamics of the populations of two interacting species, inspired by Lotka-Volterra's classical equations. The novelty of this work is that the interaction terms are non local and the interaction occurs…

Populations and Evolution · Quantitative Biology 2022-09-21 Mario I. Simoy , Marcelo N. Kuperman

In this work, we examine a kinetic framework for modeling the time evolution of size distribution densities of two populations governed by predator-prey interactions. The model builds upon the classical Boltzmann-type equations, where the…

Analysis of PDEs · Mathematics 2025-11-27 Andrea Bondesan , Marco Menale , Giuseppe Toscani , Mattia Zanella

In the analysis of complex ecosystems it is common to use random interaction coefficients, often assumed to be such that all species are statistically equivalent. In this work we relax this assumption by choosing interactions according to…

Populations and Evolution · Quantitative Biology 2023-03-08 Lyle Poley , Joseph W. Baron , Tobias Galla

The assembly and persistence of ecological communities can be understood as the result of the interaction and migration of species. Here we study a single community subject to migration from a species pool in which inter-specific…

Populations and Evolution · Quantitative Biology 2023-07-27 Matthew Dopson , Clive Emary

Dynamical systems are a valuable asset for the study of population dynamics. On this topic, much has been done since Lotka and Volterra presented the very first continuous system to understand how the interaction between two species -- the…

Dynamical Systems · Mathematics 2023-09-26 Márcia Lemos-Silva , Delfim F. M. Torres

We investigate the spreading behavior of two invasive species modeled by a Lotka-Volterra diffusive competition system with two free boundaries in a spherically symmetric setting. We show that, for the weak-strong competition case, under…

Analysis of PDEs · Mathematics 2017-10-17 Yihong Du , Chang-Hong Wu