期刊
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
卷 485, 期 2, 页码 -出版社
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jmaa.2019.123802
关键词
Lienard system; Bifurcation; Separatrix loop; Limit cycle; Global phase portrait
资金
- National Natural Science Foundation of China [11801079, 61773122]
Li and Llibre in [J. Differential Equations 252 (2012) 3142-3162] proved that a Lienard system of degree four: dx/dt = y - (ax + bx(2) + cx(3) + x(4) ), dy/dt = -x has at most one limit cycle. Moreover, the limit cycle is stable and hyperbolic if it exists. Based on their works, the aim of this paper is to give the complete bifurcation diagram and global phase portraits in the Poincare disc of this system further. First we analyze the equilibria at both finity and infinity. Then, a necessary and sufficient condition for existence of separatrix loop is founded by the rotation property. Moreover, a necessary and sufficient condition of the existence of limit cycles is also obtained. Finally, we show that the complete bifurcation diagram includes one Hopf bifurcation surface and one bifurcation surface of separatrix loop. (C) 2019 Elsevier Inc. All rights reserved.
作者
我是这篇论文的作者
点击您的名字以认领此论文并将其添加到您的个人资料中。
推荐
暂无数据