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Published online by Cambridge University Press: 14 November 2011
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).