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Uniqueness of limit cycles bounded by two invariant parabolas. (English) Zbl 1262.92003

Summary: We consider a class of cubic polynomial systems with two invariant parabolas and prove in the parameter space the existence of neighborhoods such that in one the system has a unique limit cycle and in the other the system has at most three limit cycles, bounded by the invariant parabolas.

MSC:

92B05 General biology and biomathematics
34C05 Topological structure of integral curves, singular points, limit cycles of ordinary differential equations
37N25 Dynamical systems in biology

Software:

Matlab
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References:

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