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Quadratic systems having a parabola as an integral curve. (English) Zbl 0677.34034

Summary: 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 complement).

MSC:

34C05 Topological structure of integral curves, singular points, limit cycles of ordinary differential equations
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