research_article
en
2002-06
articles
A Graph Theoretic Approach to Strong Monotonicity with respect to Polyhedral Cones
2019-04-10T15:49
2002-06-01
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.
false
https://scigraph.springernature.com/explorer/license/
95-113
http://link.springer.com/10.1023/A:1015290601993
University of Guelph
Department of Mathematics and Statistics, University of Guelph, N1G 2W1, Guelph, Ontario, Canada
Siegel
D.
Kunze
H.
Pure Mathematics
2
Mathematical Sciences
readcube_id
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dimensions_id
pub.1016589262
Springer Nature - SN SciGraph project
Department of Applied Mathematics, University of Waterloo, N2L 3G1, Waterloo, Ontario, Canada
University of Waterloo
1572-9281
Positivity
1385-1292
6
10.1023/a:1015290601993
doi