In this paper, using the Poincaré compactification technique we classify the topological phase portraits of a special kind of quadratic differential system, the Abel quadratic equations of third kind. In [1] where such investigation was presented for the first time some phase portraits were not correct and some were missing. Here we provide the complete list of non equivalent phase portraits that the Abel quadratic equations of third kind can exhibit and the bifurcation diagram of a $ 3 $-parametric subfamily of it.
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Figure 3.
Bifurcation diagram of system $(ⅰ)$ for
Figure 4.
Global phase portraits in the Poincaré disk of systems $(ⅱ)$. The phase portraits
[1] | R. Oliveira and C. Valls, On the Abel differential equations of third kind, Discrete Contin. Dyn. Syst. Ser. B, 25 (2020), 1821-1834. doi: 10.3934/dcdsb.2020004. |
Global phase portraits in the Poincaré disk of of system $(ⅰ)$
Global phase portraits in the Poincaré disk of system $(ⅰ)$
Bifurcation diagram of system $(ⅰ)$ for
Global phase portraits in the Poincaré disk of systems $(ⅱ)$. The phase portraits