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.


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


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