A Graph Theoretic Approach to Strong Monotonicity with respect to Polyhedral Cones View Full Text


Ontology type: schema:ScholarlyArticle     


Article Info

DATE

2002-06

AUTHORS

H. Kunze, D. Siegel

ABSTRACT

Consider the flow ϕt for the system of differential equations , xεΩ, Ω⊂n, Ω open. Let K(t) be an expanding polyhedral cone of constant dimension, k be a unit vector in K(0), and x0εΩ. A sufficient condition for εK(t) for t≥0 is that there exists an l so that Df(ϕt(x0))+lI leaves K(t) invariant for all t≥0. If in addition (Df(ϕt(x0))+lI)n-1 takes k into the relative interior of K(t) for all t>0 then is in the relative interior of K(t) for all t>0. The latter condition for strong monotonicity may be cumbersome to check; a graph theoretic condition which can replace it is presented in this paper. Knowledge of the facial structure of K(t) is required. The results contained in this paper are extensions of the Kamke-Müller theorem and Hirsch's theorem for strong monotone flows. Applications from chemical kinetics and epidemiology are considered. More... »

PAGES

95-113

Journal

TITLE

Positivity

ISSUE

2

VOLUME

6

Identifiers

URI

http://scigraph.springernature.com/pub.10.1023/a:1015290601993

DOI

http://dx.doi.org/10.1023/a:1015290601993

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1016589262


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