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Keywords:
stability; limit cycle; center; bifurcation
Summary:
A class of degree four differential systems that have an invariant conic $ x^2+Cy^2=1$, $C\in {\mathbb{R}}$, 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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