具有中心奇点的非线性方程相轨线的全局结构

Global Structure of the Phase Orbit of Nonlinear Differential Equations with a Center

If the singular point of linear differentiaI equations is the center, after adding nonlinear terms the singular point may still be the center or become a focus owing to the change of the topological structure. This paper discusses the global structure of the orbit in the phase plane of the nonlinear differential equation with only one singular point. We show that in the global fieds the topological structure of the phase orbit may be one of the following cases: 1) It is a bunch of the closed orbits around the singular point. 2) It is the spiral curve around the singular point. 3) There exist one or two demarcation lines. It is a bunch of the closed orbits around the singular point inside tho demarcation line and the dispersed orbit outside the demarcation line. 4) There is no limit cycle.