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1998-1999 | 25 | 4 | 449-455
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Smoothness of unordered curves in two-dimensional strongly competitive systems

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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 $C^1$.
Opis fizyczny
  • Institute of Mathematics, Wrocław University of Technology, Wybrzeże Wyspiańskiego 27, 50-370 Wrocław, Poland
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