homoclinic bifurcation

基本解释

It was proved that there exist homoclinic trajectories of a quadratic system in the range of the parameter of the saddle node bifurcation.
在鞍结分岔的参数范围内证明了具有鞍结分岔的二次系统都存在同宿轨道，得到了同宿轨道的解析表达式及其幅值与分岔参数的关系。
We developed a numerical scheme for solving the bifurcation of the nonlinear dynamic systems. The scheme is suitable for homoclinic orbits and heteroclinic orbits of dynamic systems.
提出和建立了一种非线性动力系统分岔问题的求解方法，并且对于同宿轨道和异宿轨道的求解提出了求解的格式。
The conclusion for the survival of singular homoclinic orbits extends some known results and that a periodic orbit is produced by a singular homoclinic orbit provides a new pattern of bifurcation.
文中关于奇异同宿轨道保存的结论推广了一些已知的结果，而周期轨道产生于奇异同宿轨道的分支则提供了一种新的分支类型。

同宿轨分支
In particular, the BT bifurcation is analyzed by use of a global qualitative method, and the curves of saddle-node bifurcation, Hopf bifurcation and homoclinic bifurcation are obtained at the degenerate equilibrium.
特别是其中的BT分支，我们利用全局分支理论找到了系统所具有的鞍结点分支曲线、Hopf分支曲线和同宿轨分支曲线，再现了退化平衡点附近的轨线变化规律。
同宿分岔