Global Structure of Planar Quadratic Semi-Quasi-Homogeneous Polynomial Systems

Authors

  • Zecen He
  • Haihua Liang School of Mathematics and Systems Science, Guangdong Polytechnic Normal University, Guangzhou , Guangdong 510665, China 

DOI:

https://doi.org/10.12150/jnma.2019.561

Keywords:

Semi-quasi-homogeneous, quadratic system, singular point, global phase portraits.

Abstract

This paper study the planar quadratic semi-quasi-homogeneous polynomial systems (short for PQSQHPS). By using the nilpotent singular points theorem, blow-up technique, Poincaré index formula, and Poincaré compaction method, the global phase portraits of such systems in canonical forms are discussed. Furthermore, we show that all the global phase portraits of PQSQHPS can be classed into six topological equivalence classes.

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Published

2024-04-09

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Issue

Vol. 1 No. 4 (2019)

Section

Articles

How to Cite

Global Structure of Planar Quadratic Semi-Quasi-Homogeneous Polynomial Systems. (2024). Journal of Nonlinear Modeling and Analysis, 1(4), 561-572. https://doi.org/10.12150/jnma.2019.561