Global phase portraits of Kukles differential systems with homogenous polynomial nonlinearities of degree 5 having a center

Jaume Llibre, Maurício Fronza da Silva

DOI: http://dx.doi.org/10.12775/TMNA.2016.049

Abstract


We provide 22 different global phase portraits in the Poincaré disk of all centers of the so-called Kukles polynomial differential systems of the form $\dot{x} = -y$, $\dot{y} = x+Q_5(x,y)$, where $Q_5$ is a real homogeneous polynomial of degree 5 defined in $\mathbb{R}^2$.

Keywords


Centers; Kukles; polynomial vector fields; phase portrait; Poincaré disk

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References


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