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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

In this paper, we investigate a reaction-diffusion-advection model with time delay effect. The stability/instability of the spatially nonhomogeneous positive steady state and the associated Hopf bifurcation are investigated when the given…

Dynamical Systems · Mathematics 2017-06-08 Shanshan Chen , Yuan Lou , Junjie Wei

We focus on the qualitative analysis of a reaction-diffusion with spatial heterogeneity. The system is a generalization of the well known FitzHugh-Nagumo system in which the excitability parameter is space dependent. This heterogeneity…

Dynamical Systems · Mathematics 2017-06-28 B. Ambrosio

We study a variant of the cyclic Lotka-Volterra model with three-agent interactions. Inspired by a multiplayer variation of the Rock-Paper-Scissors game, the model describes an ideal ecosystem in which cyclic competition among three species…

Populations and Evolution · Quantitative Biology 2020-10-09 Filippo Palombi , Stefano Ferriani , Simona Toti

To describe population dynamics, it is crucial to take into account jointly evolution mechanisms and spatial motion. However, the models which include these both aspects, are not still well-understood. Can we extend the existing results on…

Analysis of PDEs · Mathematics 2014-01-07 Hélène Leman , Sylvie Meleard , Sepideh Mirrahimi

In this paper, we study a three-patch two-species Lotka-Volterra competition patch model over a stream network. The individuals are subject to both random and directed movements, and the two species are assumed to be identical except for…

Populations and Evolution · Quantitative Biology 2023-06-07 Shanshan Chen , Jie Liu , Yixiang Wu

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

We explore a diffusive predator-prey system that incorporates the fear effect in advective environments. Firstly, we analyze the eigenvalue problem and the adjoint operator, considering Constant-Flux and Dirichlet (CF/D) boundary…

Dynamical Systems · Mathematics 2023-12-04 Daifeng Duan , Ben Niu , Yuan Yuan

We study a mathematical model describing the dynamics of a pluripotent stem cell population involved in the blood production process in the bone marrow. This model is a differential equation with a time delay. The delay describes the cell…

Analysis of PDEs · Mathematics 2009-04-17 Mostafa Adimy , Fabien Crauste , Shigui Ruan

Some quantities in the reaction-diffusion models from cellular biology or ecology depend on the spatial average of density functions instead of local density functions. We show that such nonlocal spatial average can induce instability of…

Analysis of PDEs · Mathematics 2020-02-03 Qingyan Shi , Junping Shi , Yongli Song

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

We deal with strongly competing multispecies systems of Lotka-Volterra type with homogeneous Dirichlet boundary conditions. For a class of nonconvex domains composed by balls connected with thin corridors, we show the occurrence of pattern…

Analysis of PDEs · Mathematics 2007-12-06 Monica Conti , Veronica Felli

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

This paper is concerned with a nonlocal diffusion Lotka-Volterra type competition model that consisting of a native species and an invasive species in a one-dimensional habitat with free boundaries. We prove the well-posedness of the system…

Dynamical Systems · Mathematics 2019-05-24 Jia-Feng Cao , Wan-Tong Li , Jie Wang

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

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

We consider a two-component competition-diffusion system with equal diffusion coefficients and inhomogeneous Dirichlet boundary conditions. When the interspecific competition parameter tends to infinity, the system solution converges to…

Analysis of PDEs · Mathematics 2007-07-13 E. C. M. Crooks , E. N. Dancer , D. Hilhorst

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

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

We investigate the global dynamics of a special case of the classical Lotka-Volterra competition-diffusion system in spatially heterogeneous environment. This model indicates that the evolution of the density of the predator is independent…

Dynamical Systems · Mathematics 2020-08-18 Leqi Chen , Shuang Chen