Smoothness of unordered curves in two-dimensional strongly competitive systems
نویسنده
چکیده
It is known that in two-dimensional systems of ODEs of the form ẋ = xf (x) with ∂f /∂x < 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. A two-dimensional system of C ordinary differential equations (ODEs)
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