用变分方法证明了二阶奇异平面哈密顿系统的同宿轨道的存在性。
The existence of a homoclinic orbit for a singular second order planar Hamiltonian system is proved by using variational methods.
采用摄动-增量法研究电机工程中一类强非线性振子的极限环和同宿轨线。
Investigates a class of strongly nonlinear oscillators in electrical engineering by using the perturbation incremental method.
运用分支方法，分析了未扰系统的同宿轨破裂以后稳定流形和不稳定流形之间的距离。
The bifurcation method was used to analyze the distance between the stable manifold and the unstable manifold after the homoclinic orbit of the unperturbated system was perturbated to break.
事实上，在已有的文献中，大部分同宿、异宿轨道分支问题都是考虑连接一个或两个双曲奇点的。
In fact, an increasing number of papers are devoted to studying bifurcations of homoclinic or heteroclinic orbits with hyperbolic equilibria.
第四节研究了扰动系统的轨道的同宿穿插并给出了参数空间的分割。
Section 4 investigates homoclinic tangles of the perturbed system and gives the partitions of the parameter space.
非双曲线型非线性系统同宿切面点和同宿横截点的存在，使得其时间序列的去噪或轨迹重影变得十分困难。
The presence of homoclinic tangencies and homoclinic intersection makes it difficult if not impossible, to denoise or shadow the trajectory of a non-hyperbolic nonlinear system.
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。
It was proved that there exist homoclinic trajectories of a quadratic system in the range of the parameter of the saddle node bifurcation.
在出生的地方他们好像是过客；从孩提时代就非常熟悉的浓荫郁郁的小巷，同小伙伴游戏其中的人烟稠密的街衢，对他们来说都不过是旅途中的一个宿站。
They are strangers in their birthplace, and the leafy lanes they have known from childhood or the populous streets in which they have played, remain but a place of passage.
在出生的地方他们好像是过客；从孩提时代就非常熟悉的浓荫郁郁的小巷，同小伙伴游戏其中的人烟稠密的街衢，对他们来说都不过是旅途中的一个宿站。
They are strangers in their birthplace, and the leafy lanes they have known from childhood or the populous streets in which they have played, remain but a place of passage.
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