Global Structure of Planar Quadratic Semi-Quasi-Homogeneous Polynomial Systems (Journal of Nonlinear Modeling and Analysis, 2024)
This paper study the planar quadratic semi-quasi-homogeneouspolynomial systems (short for PQSQHPS). By using the nilpotent singularpoints theorem, blow-up technique, Poincaré index formula, and Poincaré compaction method, the global phase portraits of such systems in canonical formsare discussed. Furthermore, we show that all the global phase portraits ofPQSQHPS can be classed into six topological equivalence classes.
Keywords: Semi-quasi-homogeneous; quadratic system; singular point; global phase portraits.