Smoothness of unordered curves in two-dimensional strongly competitive systems

• Autorzy: Janusz Mierczyński
• Języki publikacji: EN

Abstrakty

EN

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 $C^1$.

Słowa kluczowe

EN

strongly competitive system of ordinary differential equations; invariant manifold; d-curve; Lotka-Volterra system

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Applicationes Mathematicae
• Rocznik: 1998-1999
• Tom: 25
• Numer: 4
• Strony: 449-455

Daty

wydano

1999

otrzymano

1998-02-20

Twórcy

autor

Janusz Mierczyński

• Institute of Mathematics, Wrocław University of Technology, Wybrzeże Wyspiańskiego 27, 50-370 Wrocław, Poland

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