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Uniqueness of limit cycles bounded by two invariant parabolas

Eduardo Sáez; Iván Szántó — 2012

Applications of Mathematics

In this paper 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.

Coexistence of small and large amplitude limit cycles of polynomial differential systems of degree four

Eduardo Sáez; Eduardo Stange; Iván Szántó — 2007

Czechoslovak Mathematical Journal

A class of degree four differential systems that have an invariant conic $x^{2} + C y^{2} = 1$ , $C \in ℝ$ , is examined. We show the coexistence of small amplitude limit cycles, large amplitude limit cycles, and invariant algebraic curves under perturbations of the coefficients of the systems.

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