Global dynamics of planar quasi-homogeneous differential systems
Dynamical Systems
2017-08-14 v1
Abstract
In this paper we provide a new method to study global dynamics of planar quasi--homogeneous differential systems. We first prove that all planar quasi--homogeneous polynomial differential systems can be translated into homogeneous differential systems and show that all quintic quasi--homogeneous but non--homogeneous systems can be reduced to four homogeneous ones. Then we present some properties of homogeneous systems, which can be used to discuss the dynamics of quasi--homogeneous systems. Finally we characterize the global topological phase portraits of quintic quasi--homogeneous but non--homogeneous differential systems.
Keywords
Cite
@article{arxiv.1708.03437,
title = {Global dynamics of planar quasi-homogeneous differential systems},
author = {Yilei Tang and Xiang Zhang},
journal= {arXiv preprint arXiv:1708.03437},
year = {2017}
}