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Quadratic systems having a parabola as an integral curve

Published online by Cambridge University Press:  14 November 2011

Colin Christopher
Colin Christopher
Affiliation:
Department of Mathematics, The University College of Wales, Aberystwyth SY23 3BZ, U.K.
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Synopsis

The class of quadratic systems having a parabola composed of integral curves is examined. Canonical forms are found for the members of this class, and conditions are obtained, using the Bendixson's Criterion and the Poincaré–Bendixson Theorem, for the existence or non-existence of limit cycles, in the case where there is a limit cycle “inside” the parabola (that is, in the convex component of its compliment).

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 112 , Issue 1-2 , 1989 , pp. 113 - 134
Copyright
Copyright © Royal Society of Edinburgh 1989

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