Abstract
In this paper we classify the centers localized at the origin of coordinates, the cyclicity of their Hopf bifurcation and their isochronicity for the polynomial differential systems in \({\mathbb{R}^2}\) of degree d that in complex notation z = x + i y can be written as
where j is either 0 or 1, d is an arbitrary odd positive integer greater than or equal to five, \({\lambda \in \mathbb{R}}\), and \({A,B,C,D \in \mathbb{C}}\). Note that if d = 5 we obtain special families of quintic polynomial differential systems.
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Llibre, J., Valls, C. Classification of the centers, of their cyclicity and isochronicity for two classes of generalized quintic polynomial differential systems. Nonlinear Differ. Equ. Appl. 16, 657 (2009). https://doi.org/10.1007/s00030-009-0029-6
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DOI: https://doi.org/10.1007/s00030-009-0029-6