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The nonlocal Fisher equation is a diffusion-reaction equation with a nonlocal quadratic competition, which describes the reaction between distant individuals. This equation arises in evolutionary biological systems, where the arena for the…

Pattern Formation and Solitons · Physics 2018-04-25 Yehuda A. Ganan , David A. Kessler

We investigate how initial and boundary conditions influence the competition dynamics and outcome in dispersal-structured populations. The study is carried out through numerical modeling of the heterogeneous Brownian bugs model, in which…

Populations and Evolution · Quantitative Biology 2022-04-27 D. Navidad Maeso , M. Patriarca , E. Heinsalu

The paper is concerned with different types of dispersal chosen by competing species. We introduce a model with the diffusion-type term $\nabla \cdot \left[ a \nabla \left( u/P \right) \right]$ which includes some previously studied systems…

Dynamical Systems · Mathematics 2016-06-10 E. Braverman , Md. Kamrujjaman

We consider stochastic growth models to represent population subject to catastrophes. We analyze the subject from different set ups considering or not spatial restrictions, whether dispersion is a good strategy to increase the population…

Probability · Mathematics 2019-03-05 Valdivino Vargas Junior , Fábio Prates Machado , Alejandro Roldán-Correa

The goal of this work is to understand and quantify how a line with nonlocal diffusion given by an integral enhances a reaction-diffusion process occurring in the surrounding plane. This is part of a long term programme where we aim at…

Analysis of PDEs · Mathematics 2024-01-10 Henri Berestycki , Jean-Michel Roquejoffre , Luca Rossi

The current paper is concerned with the existence of spreading speeds and linear determinacy for two species competition systems with nonlocal dispersal in time and space periodic habitats. The notion of spreading speed intervals for such a…

Dynamical Systems · Mathematics 2015-12-01 Liang Kong , Nar Rawal , Wenxian Shen

We study a class of free boundary systems with nonlocal diffusion, which are natural extensions of the corresponding free boundary problems of reaction diffusion systems. As before the free boundary represents the spreading front of the…

Analysis of PDEs · Mathematics 2019-07-11 Yihong Du , Mingxin Wang , Meng Zhao

We introduce a stochastic individual model for the spatial behavior of an animal population of dispersive and competitive species, considering various kinds of biological effects, such as heterogeneity of environmental conditions, mutual…

Probability · Mathematics 2016-07-05 Joaquin Fontbona , Sylvie Méléard

The spread of new ideas, behaviors or technologies has been extensively studied using epidemic models. Here we consider a model of diffusion where the individuals' behavior is the result of a strategic choice. We study a simple coordination…

Probability · Mathematics 2015-03-17 Marc Lelarge

In this article, we study the optimization of resource distributions in a one-dimensional logistic diffusive model. The goal is to determine a distribution on a bounded one-dimensional domain that maximizes the total population at…

Analysis of PDEs · Mathematics 2025-11-21 Junyoung Heo , Yubin Lee

Resource competition is a fundamental interaction in natural communities.However little is known about competition in spatial environments where organisms are able to regulate resource distributions. Here, we analyze the competition of two…

Populations and Evolution · Quantitative Biology 2011-02-24 Alexei B. Ryabov , Bernd Blasius

We consider here a problem of population dynamics modeled on a logistic equation with both classical and nonlocal diffusion, possibly in combination with a pollination term. The environment considered is a niche with zero-flux, according to…

Analysis of PDEs · Mathematics 2021-01-08 Serena Dipierro , Edoardo Proietti Lippi , Enrico Valdinoci

Stochastic interactions generically enhance self-diffusivity in living and biological systems, e.g. optimizing navigation strategies and controlling material properties of cellular tissues and bacterial aggregates. Despite this, the…

Soft Condensed Matter · Physics 2024-01-24 Henry Alston , Thibault Bertrand

In this article, we consider a species whose population density solves the steady diffusive logistic equation in a heterogeneous environment modeled with the help of a spatially non constant coefficient standing for a resources…

Analysis of PDEs · Mathematics 2019-07-30 Idriss Mazari , Grégoire Nadin , Yannick Privat

In a geographically distributed population, assortative clustering plays an important role in evolution by modifying local environments. To examine its effects in a linear habitat, we consider a one-dimensional grid of cells, where each…

Populations and Evolution · Quantitative Biology 2021-03-16 Sunhee Chae , Nahyeon Lee , Seung Ki Baek , Hyeong-Chai Jeong

The dynamics of dispersal-structured populations, consisting of competing individuals that are characterized by different diffusion coefficients but are otherwise identical, is investigated. Competition is taken into account through…

Biological Physics · Physics 2020-04-15 E. Heinsalu , D. Navidad Maeso , M. Patriarca

We investigate the long-time behavior of phenotype-structured models describing evolutionary dynamics of asexual populations, and analyze the joint effects of nonlocal interactions and spatial resource distributions on the global dynamics…

Analysis of PDEs · Mathematics 2025-07-15 Shen Bian

We discuss the existence of stationary solutions for logistic diffusion equations of Fisher-Kolmogoroff-Petrovski-Piskunov type driven by the superposition of fractional operators in a bounded region with "hostile" environmental conditions,…

Analysis of PDEs · Mathematics 2026-03-12 Serena Dipierro , Edoardo Proietti Lippi , Caterina Sportelli , Enrico Valdinoci

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

We study a class of free boundary problems of ecological models with nonlocal and local diffusions, which are natural extensions of free boundary problems of reaction diffusion systems in there local diffusions are used to describe the…

Analysis of PDEs · Mathematics 2019-09-17 Jianping Wang , Mingxin Wang