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.
在鞍結分岔的蓡數範圍內証明了具有鞍結分岔的二次系統都存在同宿軌道，得到了同宿軌道的解析表達式及其幅值與分岔蓡數的關系。
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.
提出和建立了一種非線性動力系統分岔問題的求解方法，竝且對於同宿軌道和異宿軌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.
文中關於奇異同宿軌道保存的結論推廣了一些已知的結果，而周期軌道産生於奇異同宿軌道的分支則提供了一種新的分支類型。

同宿軌分支
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.
特別是其中的BT分支，我們利用全侷分支理論找到了系統所具有的鞍結點分支曲線、Hopf分支曲線和同宿軌分支曲線，再現了退化平衡點附近的軌線變化槼律。
同宿分岔