Smoothness of unordered curves in two-dimensional strongly competitive systems
Volume 25 / 1999
Applicationes Mathematicae 25 (1999), 449-455
DOI: 10.4064/am-25-4-449-455
Abstract
It is known that in two-dimensional systems of ODEs of the form $\dotx^i=x^if^i(x)$ with ${\partial f^i}/{\partial x^j} < 0$ (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 $C^1$.
