This paper aims to study the sufficient and necessary conditions for a generalized polynomial Liénard system with a unique equilibrium and one periodic annulus. In such a case, there are two types of equilibrium: a centre or a neighbourhood of the equilibrium consisting of a hyperbolic sector and an elliptical sector. The sufficient and necessary conditions for both cases are established and global phase portraits in the Poincaré disc are presented under certain conditions.
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Chen et al. (2024) studied this question.
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