Bifurcation diagram and global phase portraits of a family of quadratic vector fields in class I
发布时间：2020-06-03
点击次数：
DOI码：10.1007/s12346-020-00402-4
发表刊物：Qualitative Theory of Dynamical Systems
关键字：Global phase portrait · Saddle connection · Bifurcation · Generalized normal sector · Rotated vector field
摘要：We study a family of quadratic vector fields in Class I x'= y, y'= −x −αy +μx^2 − y^2, where (α,μ) ∈ R^2. To study the equilibria at infinity on the Poincaré disk of this system completely, we follow the method of generalized normal sectors of Tang and Zhang (Nonlinearity 17:1407–1426, 2004) and give further two new criterions, which allows us to obtain not only the qualitative properties of the equilibria but also asymptotic expressions of these orbits connecting the equilibria at infinity of this system. Further, the complete bifurcation diagram including saddle connection bifurcation curves of this system is given. Moreover, by qualitative properties of the equilibria, the nonexistence of limit cycle and rotated properties about α and μ, all global phase portraits on the Poincaré disk of this system are also obtained and the number is 19.
合写作者：陈海波
第一作者：贾曼
论文类型：期刊论文
通讯作者：陈和柏
论文编号：64
文献类型：J
卷号：19
页面范围：64-1-22
是否译文：否
发表时间：2020-06-03
收录刊物：SCI