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Volume 1, Issue 4
Global Structure of Planar Quadratic Semi-Quasi-Homogeneous Polynomial Systems

Zecen He & Haihua Liang

DOI: 10.12150/jnma.2019.561

J. Nonl. Mod. Anal., 1 (2019), pp. 561-572.

Published online: 2021-04

[An open-access article; the PDF is free to any online user.]

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  • 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.

  • Keywords

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

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COPYRIGHT: © Global Science Press

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@Article{JNMA-1-561, author = {He , Zecen and Liang , Haihua}, title = {Global Structure of Planar Quadratic Semi-Quasi-Homogeneous Polynomial Systems}, journal = {Journal of Nonlinear Modeling and Analysis}, year = {2021}, volume = {1}, number = {4}, pages = {561--572}, 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.

}, issn = {2562-2862}, doi = {https://doi.org/10.12150/jnma.2019.561}, url = {http://global-sci.org/intro/article_detail/jnma/18840.html} }
TY - JOUR T1 - Global Structure of Planar Quadratic Semi-Quasi-Homogeneous Polynomial Systems AU - He , Zecen AU - Liang , Haihua JO - Journal of Nonlinear Modeling and Analysis VL - 4 SP - 561 EP - 572 PY - 2021 DA - 2021/04 SN - 1 DO - http://doi.org/10.12150/jnma.2019.561 UR - https://global-sci.org/intro/article_detail/jnma/18840.html KW - Semi-quasi-homogeneous, quadratic system, singular point, global phase portraits. AB -

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.

Zecen He & Haihua Liang. (1970). Global Structure of Planar Quadratic Semi-Quasi-Homogeneous Polynomial Systems. Journal of Nonlinear Modeling and Analysis. 1 (4). 561-572. doi:10.12150/jnma.2019.561
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