Spatial heterogeneity of resources versus Lotka-Volterra dynamics

DOI10.1006/jdeq.2001.4157zbMath1023.35047OpenAlexW1990636052MaRDI QIDQ1864627

Yuan Lou, Konstantin Mischaikow, Vivian Hutson

Publication date: 18 March 2003

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jdeq.2001.4157

zbMATH Keywords

zero Neumann boundary conditionscompetitive exclusionstability of equilibriacoexistence solutions

Mathematics Subject Classification ID

Related Items (46)

Global dynamics of the Lotka-Volterra competition-diffusion system with equal amount of total resources. II ⋮ A diffusive predator-prey model in heterogeneous environment ⋮ Bifurcation branch of stationary solutions for a Lotka-Volterra cross-diffusion system in a spatially heterogeneous environment ⋮ A SIS reaction-diffusion model with a free boundary condition and nonhomogeneous coefficients ⋮ A singular perturbation result in competition theory ⋮ A diffusive predator-prey model with a protection zone ⋮ Loops and branches of coexistence states in a Lotka--Volterra competition model ⋮ Stochastic Lotka-Volterra competitive reaction-diffusion systems perturbed by space-time white noise: modeling and analysis ⋮ Spatial versus non-spatial dynamics for diffusive Lotka-Volterra competing species models ⋮ Global dynamics of the Lotka-Volterra competition-diffusion system with equal amount of total resources. III ⋮ Spatial-temporal dynamics of a diffusive Lotka-Volterra competition model with a shifting habitat II: Case of faster diffuser being a weaker competitor ⋮ Qualitative analysis of a Lotka-Volterra predator-prey system with migration ⋮ Dynamics of a periodic-parabolic Lotka-Volterra competition-diffusion system in heterogeneous environments ⋮ Dynamical analysis of a competition‐diffusion‐advection system with Dirichlet boundary conditions ⋮ Global dynamics of a general Lotka-Volterra competition-diffusion system in heterogeneous environments ⋮ Realization of prescribed patterns in the competition model. ⋮ Fish-hook shaped global bifurcation branch of a spatially heterogeneous cooperative system with cross-diffusion ⋮ Bifurcation branch of stationary solutions in a general predator-prey system with prey-taxis ⋮ Global directed dynamics of a Lotka-Volterra competition-diffusion system ⋮ The stability of bifurcating steady states for a spatially heterogeneous cooperative system with cross-diffusion ⋮ Evolution of dispersal in open advective environments ⋮ A diffusive competition model with a protection zone ⋮ A nonlocal diffusion model with free boundaries in spatial heterogeneous environment ⋮ Positive solutions of a diffusive prey-predator model in a heterogeneous environment ⋮ Existence and stability of coexistence states for a reaction-diffusion-advection model ⋮ Competition in periodic media. I: Existence of pulsating fronts ⋮ Hopf bifurcation and pattern formation in a delayed diffusive logistic model with spatial heterogeneity ⋮ Invasion and coexistence of competition-diffusion-advection system with heterogeneous vs homogeneous resources ⋮ On the effects of migration and spatial heterogeneity on single and multiple species ⋮ Numerical solutions of inverse spatial Lotka-Volterra systems ⋮ Convergence in competition models with small diffusion coefficients ⋮ An optimization problem and its application in population dynamics ⋮ Resonance Phenomena in a Singular Perturbation Problem in the Case of Exchange of Stabilities ⋮ On steady state of some Lotka-Volterra competition-diffusion-advection model ⋮ Global Dynamics of the Lotka-Volterra Competition-Diffusion System: Diffusion and Spatial Heterogeneity I ⋮ Steady-State Problem of an S-K-T Competition Model with Spatially Degenerate Coefficients ⋮ Dynamics of a diffusive competition model in spatially heterogeneous environment ⋮ Spreading Speeds and Linear Determinacy for Two Species Competition Systems with Nonlocal Dispersal in Periodic Habitats ⋮ The effect of initial values on extinction or persistence in degenerate diffusion competition systems ⋮ Effect of a protection zone in the diffusive Leslie predator-prey model ⋮ On a Lotka-Volterra competition diffusion model with advection ⋮ SINGULARLY PERTURBED ELLIPTIC SYSTEM MODELING THE COMPETITIVE INTERACTIONS FOR A SINGLE RESOURCE ⋮ Global stability of nonhomogeneous equilibrium solution for the diffusive Lotka-Volterra competition model ⋮ Patterns Versus Spatial Heterogeneity—From a Variational Viewpoint ⋮ Global dynamics of a two-species Lotka-Volterra competition-diffusion-advection system with general carrying capacities and intrinsic growth rates. II: Different diffusion and advection rates ⋮ The ground state of a Gross-Pitaevskii energy with general potential in the Thomas-Fermi limit

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Large amplitude stationary solutions to a chemotaxis system
• The evolution of slow dispersal rates: a reaction diffusion model
• Bifurcation, perturbation of simple eigenvalues, and linearized stability

This page was built for publication: Spatial heterogeneity of resources versus Lotka-Volterra dynamics