On a Lotka-Volterra competition model: the effects of advection and spatial variation

DOI10.1007/s00526-016-1021-8zbMath1366.35088OpenAlexW2436806495MaRDI QIDQ502215

Xiao-Qiang Zhao, Peng Zhou

Publication date: 3 January 2017

Published in: Calculus of Variations and Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00526-016-1021-8

zbMATH Keywords

advectionLotka-Volterra systemheterogeneous environment

Mathematics Subject Classification ID

Reaction-diffusion equations (35K57) Population dynamics (general) (92D25) Nonlinear initial, boundary and initial-boundary value problems for nonlinear parabolic equations (35K61)

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II: Different diffusion and advection rates

Cites Work

• Unnamed Item
• Unnamed Item
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• Unnamed Item
• Climate and competition: the effect of moving range boundaries on habitat invasibility
• The effects of diffusion and spatial variation in Lotka-Volterra competition-diffusion system. II: The general case
• Evolution of dispersal in open advective environments
• Qualitative analysis for a Lotka-Volterra competition system in advective homogeneous environment
• Concentration phenomena of a semilinear elliptic equation with large advection in an ecological model
• The effects of diffusion and spatial variation in Lotka-Volterra competition-diffusion system I: Heterogeneity vs. homogeneity
• Effects of heterogeneity on spread and persistence in rivers
• The effects of spatial heterogeneity in population dynamics
• Movement toward better environments and the evolution of rapid diffusion
• Evolution of conditional dispersal: a reaction-diffusion-advection model
• Limiting profiles of semilinear elliptic equations with large advection in population dynamics
• A theorem on elliptic differential inequalities with an application to gradient bounds
• The evolution of slow dispersal rates: a reaction diffusion model
• On the effects of spatial heterogeneity on the persistence of interacting species
• Realization of prescribed patterns in the competition model.
• Elliptic partial differential equations of second order
• Effects of a degeneracy in the competition model. II: Perturbation and dynamical behaviour
• Multiple reversals of competitive dominance in ecological reserves via external habitat degradation
• Does movement toward better environments always benefit a population?
• Evolution of a semilinear parabolic system for migration and selection in population genetics
• Evolution of dispersal in advective homogeneous environment: the effect of boundary conditions
• Spatial patterns and coexistence mechanisms in systems with unidirectional flow
• Persistence, spread and the drift paradox
• A remark on the global dynamics of competitive systems on ordered Banach spaces
• Global Dynamics of the Lotka-Volterra Competition-Diffusion System: Diffusion and Spatial Heterogeneity I
• Limiting Profiles of Semilinear Elliptic Equations with Large Advection in Population Dynamics II
• On a nonlocal reaction–diffusion–advection equation modelling phytoplankton dynamics
• Evolution of dispersal in closed advective environments
• Principal eigenvalue and eigenfunctions of an elliptic operator with large advection and its application to a competition model
• On an abstract competition model and applications
• Competing Species near a Degenerate Limit
• Spatial Ecology via Reaction‐Diffusion Equations
• Competitive exclusion and coexistence for competitive systems on ordered Banach spaces
• Uniqueness and Complete Dynamics in Heterogeneous Competition-Diffusion Systems
• Effects of diffusion and advection on the smallest eigenvalue of an elliptic operator and their applications
• Should a Park Be an Island?
• Concentration Phenomena in a Nonlocal Quasi-linear Problem Modelling Phytoplankton I: Existence
• Concentration Phenomena in a Nonlocal Quasi-linear Problem Modelling Phytoplankton II: Limiting Profile
• The Role of Advection in a Two-Species Competition Model: A Bifurcation Approach
• On a Nonlocal Reaction-Diffusion Problem Arising from the Modeling of Phytoplankton Growth
• Advection-mediated coexistence of competing species
• The Effect of Dispersal Patterns on Stream Populations
• Dynamical systems in population biology