It is known that in two-dimensional systems of ODEs of the form with (strongly competitive systems), boundaries of the basins of repulsion of equilibria consist of invariant Lipschitz curves, unordered with respect to the coordinatewise (partial) order. We prove that such curves are in fact of class .
@article{bwmeta1.element.bwnjournal-article-zmv25i4p449bwm,
author = {Janusz Mierczy\'nski},
title = {Smoothness of unordered curves in two-dimensional strongly competitive systems},
journal = {Applicationes Mathematicae},
volume = {26},
year = {1999},
pages = {449-455},
zbl = {1005.34042},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-zmv25i4p449bwm}
}
Mierczyński, Janusz. Smoothness of unordered curves in two-dimensional strongly competitive systems. Applicationes Mathematicae, Tome 26 (1999) pp. 449-455. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-zmv25i4p449bwm/
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