A cubic system with a limit cycle bounded by two invariant parabolas. (English) Zbl 1207.34038

Summary: We show the existence of a cubic system having at least one limit cycle bounded by two invariant parabolas. We also obtain necessary and sufficient conditions for the critical point in the interior of the bounded region to be a center.


34C05 Topological structure of integral curves, singular points, limit cycles of ordinary differential equations
34C07 Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert’s 16th problem and ramifications) for ordinary differential equations


Mathematica; Matlab
Full Text: DOI


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