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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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