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We study a diffusive Lotka-Volterra competition system with advection under Neumann boundary conditions. Our system models a competition relationship that one species escape from the region of high population density of their competitors in…

Analysis of PDEs · Mathematics 2015-05-28 Chunyi Gai , Qi Wang , Jingda Yan

This paper explains the uniqueness of positive steady state of general Lotka-Volterra competition model of two species of animals in the same environment.

Analysis of PDEs · Mathematics 2008-06-24 Joon Hyuk Kang

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

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

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

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

The forces which drive growth, development, survival and change within an ecological system involving a predator and prey specie are not easily addressed in the field. To better understand the dynamics in the system, ecologists have turned…

General Mathematics · Mathematics 2025-10-14 Arhonefe Joseph Ogethakpo , Sunday Amaju Ojobor

We consider a model for a population in a heterogeneous environment, with logistic type local population dynamics, under the assumption that individuals can switch between two different nonzero rates of diffusion. Such switching behavior…

Analysis of PDEs · Mathematics 2020-01-14 Robert Stephen Cantrell , Chris Cosner , Xiao Yu

We study the propagation speed of bistable traveling waves in the classical two-component diffusive Lotka-Volterra system under strong competition. From an ecological perspective, the sign of the propagation speed determines the long-term…

Analysis of PDEs · Mathematics 2025-10-17 Ken-Ichi Nakamura , Toshiko Ogiwara

This paper presents a study of the two-predators-two-preys discrete-time Lotka-Volterra model with self- inhibition terms for preys with direct applications to ecological problems. Parameters in the model are modified so that each of them…

Dynamical Systems · Mathematics 2012-11-27 Hanbaek Lyu , Piotr Grzegorz Jablonski

Owing to the analogies between the problem of wealth redistribution with taxation in a multi-agent society, we introduce and discuss a kinetic model describing the statistical distributions in time of the sizes of groups of biological…

Populations and Evolution · Quantitative Biology 2023-11-15 Giuseppe Toscani , Mattia Zanella

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

Motivated by the traditional Lotka-Volterra competitive models, this paper proposes and analyzes a class of stochastic reaction-diffusion partial differential equations. In contrast to the models in the literature, the new formulation…

Probability · Mathematics 2021-05-10 N. N. Nguyen , G. Yin

We study the effect of speciation, i.e. the introduction of new species through evolution into communities, in the setting of predator-prey systems. Predator-prey dynamics is classically well modeled by Lotka-Volterra equations, also when…

Populations and Evolution · Quantitative Biology 2025-03-20 Christian Hamster , Jorik Schaap , Peter van Heijster , Joshua Dijksman

The current series of two papers focus on a 3-dimensional Lotka-Volterra competition model of differential equations with seasonal succession, which exhibits that populations experience an external periodically forced environment. We are…

Dynamical Systems · Mathematics 2023-12-19 Lei Niu , Yi Wang , Xizhuang Xie

This paper is concerned with a diffusive Lotka-Volterra type competition system with a free boundary in one space dimension. Such a system may be used to describe the invasion of a new species into the habitat of a native competitor. We…

Analysis of PDEs · Mathematics 2017-10-17 Zhiguo Wang , Hua Nie , Yihong Du

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

We study a modified version of a prey-predator system with modified Leslie-Gower and Holling type II functional response studied by M.A. Aziz-Alaoui and M. Daher-Okiye. The modification consists in incorporating a refuge for preys, and…

Probability · Mathematics 2019-04-09 Safia Slimani , Paul Raynaud de Fitte , Islam Boussaada

We investigate the Lotka-Volterra model for predator-prey competition with a finite carrying capacity that varies periodically in time, modeling seasonal variations in nutrients or food resources. In the absence of time variability, the…

Pattern Formation and Solitons · Physics 2026-05-05 Mohamed Swailem , Alastair M. Rucklidge

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