# Smoothness of unordered curves in two-dimensional strongly competitive systems

Applicationes Mathematicae (1999)

- Volume: 25, Issue: 4, page 449-455
- ISSN: 1233-7234

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topMierczyński, Janusz. "Smoothness of unordered curves in two-dimensional strongly competitive systems." Applicationes Mathematicae 25.4 (1999): 449-455. <http://eudml.org/doc/219218>.

@article{Mierczyński1999,

abstract = {It is known that in two-dimensional systems of ODEs of the form $^i=x^if^i(x)$ 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 $C^1$.},

author = {Mierczyński, Janusz},

journal = {Applicationes Mathematicae},

keywords = {strongly competitive system of ordinary differential equations; invariant manifold; d-curve; Lotka-Volterra system; smoothness; unordered curves; two-dimensional strongly competitive systems; equilibria; invariant Lipschitz curves},

language = {eng},

number = {4},

pages = {449-455},

title = {Smoothness of unordered curves in two-dimensional strongly competitive systems},

url = {http://eudml.org/doc/219218},

volume = {25},

year = {1999},

}

TY - JOUR

AU - Mierczyński, Janusz

TI - Smoothness of unordered curves in two-dimensional strongly competitive systems

JO - Applicationes Mathematicae

PY - 1999

VL - 25

IS - 4

SP - 449

EP - 455

AB - It is known that in two-dimensional systems of ODEs of the form $^i=x^if^i(x)$ 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 $C^1$.

LA - eng

KW - strongly competitive system of ordinary differential equations; invariant manifold; d-curve; Lotka-Volterra system; smoothness; unordered curves; two-dimensional strongly competitive systems; equilibria; invariant Lipschitz curves

UR - http://eudml.org/doc/219218

ER -

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