Smoothness of unordered curves in two-dimensional strongly competitive systems

Volume 25 / 1999

Janusz Mierczyński 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 $C^1$.

Authors

  • Janusz Mierczyński

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