This paper is devoted to the complete classification of global phase portraits (short for GPP) of quasi-homogeneous but non-homogeneous coprime planar quintic polynomial differential systems (short for QCQS). We firstly… Click to show full abstract
This paper is devoted to the complete classification of global phase portraits (short for GPP) of quasi-homogeneous but non-homogeneous coprime planar quintic polynomial differential systems (short for QCQS). We firstly study the canonical forms of QCQS. It is shown that these canonical forms can have 0, 1, 2, 4 parameters. Then, we investigate the global topological structures of all canonical forms, by using the quasi-homogeneous blow-up technique for the finite singularities and the Poincaré–Lyapunov compactification for the infinite singularities. We finally perform a topological classification for the set of GPP.
Journal Title: Qualitative Theory of Dynamical Systems
Year Published: 2017
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