Spectral Radii and Collatz–Wielandt Numbers for Homogeneous Order-preserving Maps and the Monotone Companion Norm

DOI10.1007/978-3-319-27842-1_26zbMath1411.47012arXiv1406.6657OpenAlexW2523096754MaRDI QIDQ4645878

Horst R. Thieme

Publication date: 11 January 2019

Published in: Trends in Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1406.6657

zbMATH Keywords

normal conecomparison theoremsbasic reproduction numberKrein-Rutman theoremcone spectral radiushomogeneous maprank structureCollatz-Wielandt numbersnonlinear eigenvectorsordered normed vector spacepopulation models with mating

Mathematics Subject Classification ID

Nonlinear spectral theory, nonlinear eigenvalue problems (47J10) Monotone and positive operators on ordered Banach spaces or other ordered topological vector spaces (47H07) Applications of operator theory in chemistry and life sciences (47N60)

Related Items (13)

The principal eigenvalue of some \(n\)th order linear boundary value problems ⋮ Eigenfunctionals of homogeneous order-preserving maps with applications to sexually reproducing populations ⋮ From homogeneous eigenvalue problems to two-sex population dynamics ⋮ A periodic-parabolic droop model for two species competition in an unstirred chemostat ⋮ Single species growth consuming inorganic carbon with internal storage in a poorly mixed habitat ⋮ Reproduction number versus turnover number in structured discrete-time population models ⋮ Measures under the flat norm as ordered normed vector space ⋮ Eigenvectors of homogeneous order-bounded order-preserving maps ⋮ Discrete-time population dynamics on the state space of measures ⋮ Discrete-time population dynamics of spatially distributed semelparous two-sex populations ⋮ Persistent discrete-time dynamics on measures ⋮ On the spectral theory of positive operators and PDE applications ⋮ The basic reproduction number \(R_0\) in time-heterogeneous environments

Cites Work

• Persistence and critical domain size for diffusing populations with two sexes and short reproductive season
• Eigenfunctionals of homogeneous order-preserving maps with applications to sexually reproducing populations
• Persistence and extinction of diffusing populations with two sexes and short reproductive season
• Positive dynamical systems in discrete time. Theory, models and applications
• Generalizing the Kreĭn-Rutman theorem, measures of noncompactness and the fixed point index
• Genealogy with seasonality, the basic reproduction number, and the influenza pandemic
• Halbgeordnete lokalkonvexe Vektorräume. II
• On the definition and the computation of the basic reproduction ratio \(R_ 0\) in models for infectious diseases in heterogeneous populations
• Asymptotic fixed point theory and the beer barrel theorem
• An extinction/persistence threshold for sexually reproducing populations: the cone spectral radius
• On the Collatz-Wielandt numbers and the local spectral radius of a nonnegative operator
• Pair formation in age-structured populations
• Eigenvalues for a class of homogeneous cone maps arising from max-plus operators
• Denjoy-Wolff theorems for Hilbert's and Thompson's metric spaces
• Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission
• An elementary proof of the Hopf inequality for positive operators
• Unzerlegbare, nicht negative Matrizen
• Positive Transformationen in lokalkonvexen halbgeordneten Vektorräumen
• Continuity of the cone spectral radius
• Nonlinear Perron–Frobenius Theory
• Extensions of Jentzsch's Theorem
• Linear Operators in Complete Positive Cones
• Eigenvectors of Order-Preserving Linear Operators
• Gender-Structured Population Modeling
• Applications of the Birkhoff–Hopf theorem to the spectral theory of positive linear operators
• On the definition of the cone spectral radius
• Spectral Bound and Reproduction Number for Infinite-Dimensional Population Structure and Time Heterogeneity
• On the Eigenvectors of Some Not-Necessarily-Linear Transformations
• On Certain Contraction Mappings in a Partially Ordered Vector Space
• Endomorphisms of a Partially Ordered Vector Space Without Order Unit
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• Unnamed Item
• Unnamed Item
• Unnamed Item
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• Unnamed Item
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