On principal spectrum points/principal eigenvalues of nonlocal dispersal operators and applications

DOI10.3934/dcds.2015.35.1665zbMath1302.45004arXiv1309.4753OpenAlexW2962750330MaRDI QIDQ484400

Wenxian Shen, Xiaoxia Xie

Publication date: 7 January 2015

Published in: Discrete and Continuous Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1309.4753

zbMATH Keywords

principal eigenvaluespatial inhomogeneitydispersal distancedispersal ratenonlocal dispersal operatorprincipal spectrum pointtwo species competition system

Mathematics Subject Classification ID

Population dynamics (general) (92D25) Asymptotics of solutions to integral equations (45M05) Integral operators (47G10) Eigenvalue problems for integral equations (45C05) Positive solutions of integral equations (45M20)

Related Items (32)

Nonlocal dispersal equations in time-periodic media: principal spectral theory, limiting properties and long-time dynamics ⋮ Principal eigenvalue, maximum principles and linear stability for nonlocal diffusion equations in metric measure spaces ⋮ On the definition and the properties of the principal eigenvalue of some nonlocal operators ⋮ Dynamics for a two-phase free boundary system in an epidemiological model with couple nonlocal dispersals ⋮ Principal spectral theory and asynchronous exponential growth for age-structured models with nonlocal diffusion of Neumann type ⋮ The generalised principal eigenvalue of time-periodic nonlocal dispersal operators and applications ⋮ The spectral bound and basic reproduction ratio for nonlocal dispersal cooperative problems ⋮ Criteria for the existence and lower bounds of principal eigenvalues of time periodic nonlocal dispersal operators and applications ⋮ Threshold dynamics of a time-periodic nonlocal dispersal SIS epidemic model with Neumann boundary conditions ⋮ Principal spectral theory of time‐periodic nonlocal dispersal operators of Neumann type ⋮ Principal spectral theory for nonlocal systems and applications to stem cell regeneration models ⋮ Asymptotic limits of the principal spectrum point of a nonlocal dispersal cooperative system and application to a two-stage structured population model ⋮ The nonlocal dispersal equation with seasonal succession ⋮ Principal spectral theory and variational characterizations for cooperative systems with nonlocal and coupled diffusion ⋮ Principal spectral theory in multigroup age-structured models with nonlocal diffusion ⋮ Exponential quasi-ergodicity for processes with discontinuous trajectories ⋮ Study of a Mixed Dispersal Population Dynamics Model ⋮ Global stability and pattern formation in a nonlocal diffusive Lotka-Volterra competition model ⋮ Criteria for the existence of principal eigenvalues of time periodic cooperative linear systems with nonlocal dispersal ⋮ Estimates for principal Lyapunov exponents: a survey ⋮ Asymptotic behaviors for nonlocal diffusion equations about the dispersal spread ⋮ Can a population survive in a shifting environment using non-local dispersion? ⋮ Approximations of random dispersal operators/equations by nonlocal dispersal operators/equations ⋮ On eigenvalue problems arising from nonlocal diffusion models ⋮ Concentration phenomenon in some non-local equation ⋮ Spectral theory for nonlocal dispersal operators with time periodic indefinite weight functions and applications ⋮ Spatial pattern formation in activator-inhibitor models with nonlocal dispersal ⋮ Nonlocal dispersal equations with almost periodic dependence. I. Principal spectral theory ⋮ The evolution dynamics of an impulsive hybrid population model with spatial heterogeneity ⋮ Nonlinear nonlocal reaction-diffusion problem with local reaction ⋮ Generalized principal eigenvalues on \({\mathbb{R}}^d\) of second order elliptic operators with rough nonlocal kernels ⋮ Effects of boundary and spatial heterogeneity on nonlocal dispersal equations

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