homoclinic bifurcation

基本解釋

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(jié)分岔的參數(shù)范圍內(nèi)證明了具有鞍結(jié)分岔的二次系統(tǒng)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參數(shù)的關(guān)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(tǒng)分岔問題的求解方法，并且對于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(guān)于奇異同宿軌道保存的結(jié)論推廣了一些已知的結(jié)果，而周期軌道產(chǎn)生于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，我們利用全局分支理論找到了系統(tǒng)所具有的鞍結(jié)點分支曲線、Hopf分支曲線和同宿軌分支曲線，再現(xiàn)了退化平衡點附近的軌線變化規(guī)律。
同宿分岔