Global stability and pattern formation in a nonlocal diffusive Lotka-Volterra competition model
type: Item
instance of: scholarly article
title: Global stability and pattern formation in a nonlocal diffusive Lotka-Volterra competition model
zbMATH Open document ID: 1397.35124
author: Wenjie Ni
author: Junping Shi
author: Mingxin Wang
published in: Journal of Differential Equations
publication date: 2018-03-22T00:00:00Z
review text: A diffusive Lotka-Volterra competition model with nonlocal intraspecific and interspecific competition between species is formulated and analyzed. The nonlocal competition strength is assumed to be determined by a diffusion kernel function to model the movement pattern of the biological species. It is shown that when there is no nonlocal intraspecific competition, the dynamics properties of nonlocal diffusive competition problem are similar to those of classical diffusive Lotka-Volterra competition model regardless of the strength of nonlocal interspecific competition. Global stability of nonnegative constant equilibria are proved using Lyapunov or upper-lower solution methods. On the other hand, strong nonlocal intraspecific competition increases the system spatiotemporal dynamic complexity. For the weak competition case, the nonlocal diffusive competition model may possess nonconstant positive equilibria for some suitably large nonlocal intraspecific competition coefficients. Reviewer's remark: In this reviewer's opinion a missing relevant reference is [\textit{J. Medlock} and \textit{M. Kot}, Math. Biosci. 184, No. 2, 201--222 (2003; Zbl 1036.92030)].
reviewed by: E. Ahmed
Mathematics Subject Classification ID: 35K51
Mathematics Subject Classification ID: 35B40
Mathematics Subject Classification ID: 35K57
Mathematics Subject Classification ID: 35K58
Mathematics Subject Classification ID: 92C15
Mathematics Subject Classification ID: 92D25
Mathematics Subject Classification ID: 92D40
Mathematics Subject Classification ID: 35Q92
zbMATH DE Number: 6852255
zbMATH Keywords: diffusive Lotka-Volterra competition model
zbMATH Keywords: nonlocal interaction
zbMATH Keywords: global stability
zbMATH Keywords: non-constant equilibrium solution
MaRDI profile type: Publication
full work available at URL: j.jde.2018.02.002
OpenAlex ID: W2790451536
cites work: Q4381940
cites work: Q4225180
cites work: Existence of positive solution of a nonlocal logistic population model
cites work: Q3262986
cites work: Existence, uniqueness and stability of the stationary solution to a nonlocal evolution equation arising in population dispersal
cites work: On the definition and the properties of the principal eigenvalue of some nonlocal operators
cites work: Dynamics of a strongly nonlocal reaction–diffusion population model
cites work: Spatial Structures and Periodic Travelling Waves in an Integro-Differential Reaction-Diffusion Population Model
cites work: Spatial Ecology via Reaction‐Diffusion Equations
cites work: Advection-mediated coexistence of competing species
cites work: On the stability of homogeneous steady states of a chemotaxis system with logistic growth term
cites work: Stability and Hopf bifurcation in a diffusive logistic population model with nonlocal delay effect
cites work: Global attractivity of equilibrium in Gierer-Meinhardt system with activator production saturation and gene expression time delays
cites work: Dynamics of a reaction-diffusion-advection model for two competing species
cites work: Asymptotic estimates for the spatial segregation of competitive systems
cites work: Nonlinear heterogeneous problems with nonlocal reaction term
cites work: On a simple criterion for the existence of a principal eigenfunction of some nonlocal operators
cites work: On a non-local equation arising in population dynamics
cites work: Bifurcation from simple eigenvalues
cites work: Bifurcation, perturbation of simple eigenvalues, and linearized stability
cites work: Dynamics of strongly competing systems with many species
cites work: The evolution of slow dispersal rates: a reaction diffusion model
cites work: Semi-wave and spreading speed for the diffusive competition model with a free boundary
cites work: Local vs. non-local interactions in population dynamics
cites work: Travelling front solutions of a nonlocal Fisher equation
cites work: Spatio-temporal pattern formation in a nonlocal reaction-diffusion equation
cites work: Global dynamics of the Lotka-Volterra competition-diffusion system: diffusion and spatial heterogeneity. I
cites work: A Mathematical Theory for Single-Nutrient Competition in Continuous Cultures of Micro-Organisms
cites work: Competitive exclusion and coexistence for competitive systems on ordered Banach spaces
cites work: The spatial homogeneity of stable equilibria of some reaction-diffusion systems on convex domains
cites work: Discrete-time travelling waves: Ecological examples
cites work: Uniqueness and Complete Dynamics in Heterogeneous Competition-Diffusion Systems
cites work: On eigenvalue problems arising from nonlocal diffusion models
cites work: Analysis.
cites work: Large amplitude stationary solutions to a chemotaxis system
cites work: Imperfect transcritical and pitchfork bifurcations
cites work: On the effects of migration and spatial heterogeneity on single and multiple species
cites work: Diffusion vs cross-diffusion: An elliptic approach
cites work: Qualitative analysis for a Lotka-Volterra competition system in advective homogeneous environment
cites work: Evolution of dispersal in advective homogeneous environment: the effect of boundary conditions
cites work: Pattern formation in competition-diffusion systems in nonconvex domains
cites work: Spatial segregation in competitive interaction-diffusion equations
cites work: Coexistence problem for two competing species models with density- dependent diffusion
cites work: Long time behavior of a diffusive competition model
cites work: Q3093930
cites work: Non-constant positive steady states of a predator-prey system with non-monotonic functional response and diffusion
cites work: Strategy and stationary pattern in a three-species predator--prey model
cites work: On principal spectrum points/principal eigenvalues of nonlocal dispersal operators and applications
cites work: Existence and uniqueness of steady state solutions of a nonlocal diffusive logistic equation
cites work: Q3690646
cites work: Non-constant positive steady states of the Sel'kov model.
cites work: A diffusive logistic equation with a free boundary and sign-changing coefficient in time-periodic environment
cites work: Note on the Lyapunov functional method

Global stability and pattern formation in a nonlocal diffusive Lotka-Volterra competition model (cites work)
cites work: On logistic diffusion equations with nonlocal interaction terms

Global stability and pattern formation in a nonlocal diffusive Lotka-Volterra competition model (cites work)
cites work: On a Lotka-Volterra competition model: the effects of advection and spatial variation

Global stability and pattern formation in a nonlocal diffusive Lotka-Volterra competition model (cites work)
cites work: On a Lotka-Volterra competition system: diffusion vs advection

Global stability and pattern formation in a nonlocal diffusive Lotka-Volterra competition model (cites work)
cites work: Evolution of passive movement in advective environments: general boundary condition

Global stability and pattern formation in a nonlocal diffusive Lotka-Volterra competition model (DOI)
DOI: 10.1016/J.JDE.2018.02.002

Global stability and pattern formation in a nonlocal diffusive Lotka-Volterra competition model (Recommended article)
Recommended article: The Lotka-Volterra models with non-local reaction terms
Similarity Score: 0.88942206
Recommender Run: Recommender Run 2

Global stability and pattern formation in a nonlocal diffusive Lotka-Volterra competition model (Recommended article)
Recommended article: Global Dynamics of a Lotka–Volterra Competition Diffusion System with Nonlocal Effects
Similarity Score: 0.8823832
Recommender Run: Recommender Run 2

Global stability and pattern formation in a nonlocal diffusive Lotka-Volterra competition model (Recommended article)
Recommended article: Traveling waves for nonlocal Lotka-Volterra competition systems
Similarity Score: 0.86789453
Recommender Run: Recommender Run 2

Global stability and pattern formation in a nonlocal diffusive Lotka-Volterra competition model (Recommended article)
Recommended article: The linear and nonlinear diffusion of the competitive Lotka-Volterra model
Similarity Score: 0.8660588
Recommender Run: Recommender Run 2

Global stability and pattern formation in a nonlocal diffusive Lotka-Volterra competition model (Recommended article)
Recommended article: Positive solutions of a Lotka-Volterra competition model with cross-diffusion
Similarity Score: 0.8620646
Recommender Run: Recommender Run 2

Global stability and pattern formation in a nonlocal diffusive Lotka-Volterra competition model (Recommended article)
Recommended article: Global dynamics of the Lotka-Volterra competition-diffusion system: diffusion and spatial heterogeneity. I
Similarity Score: 0.85643184
Recommender Run: Recommender Run 2

Global stability and pattern formation in a nonlocal diffusive Lotka-Volterra competition model (Recommended article)
Recommended article: The dynamics of a Lotka-Volterra competition model with nonlocal diffusion and free boundaries
Similarity Score: 0.8521524
Recommender Run: Recommender Run 2

Global stability and pattern formation in a nonlocal diffusive Lotka-Volterra competition model (Recommended article)
Recommended article: Global stability of nonhomogeneous equilibrium solution for the diffusive Lotka-Volterra competition model
Similarity Score: 0.8515967
Recommender Run: Recommender Run 2

Global stability and pattern formation in a nonlocal diffusive Lotka-Volterra competition model (Recommended article)
Recommended article: Uniqueness and Complete Dynamics in Heterogeneous Competition-Diffusion Systems
Similarity Score: 0.84857154
Recommender Run: Recommender Run 2

Global stability and pattern formation in a nonlocal diffusive Lotka-Volterra competition model (Recommended article)
Recommended article: Competing species systems with diffusion and large interactions
Similarity Score: 0.8485573
Recommender Run: Recommender Run 2