稳定流形

讨论平面上OLG模型的均衡解的稳定性，并利用一个类似稳定流形定理的结论，把二维动力系统化为一维动力系统，从而在整体上研究带有国家财政赤字的OLG模型。

The stability of the equilibrium solution is discussed in the OLG model of planner system , With a result close to the stable manifold theorem , the dimension of the problem is reduced , then the paper provides a global analysis of the dynamics of the model .

基于稳定流形变换的电力系统暂态稳定性计算

Transient Stability Calculation of Electric Power System Based on the Stable Manifold Transformation

本文的优点是给出了更明确的解，并把次谐分支的Melnikov函数与稳定流形与不稳定流形横截相交的Melnikov函数统一成为一个公式。

The advantage of our paper is to give a more explicit solution and to make Melnikov function for the subharmonics bifurcation and Melnikov function which the stable manifolds and unstable manifolds intersect transversely into a formula .

树映射的不稳定流形，非游荡集与拓扑熵

Unstable Manifolds , Nonwandering Sets and Topological Entropy of Tree Maps

线性序拓扑空间上不稳定流形的映射性质

Features of Mapping of a Unstable Manifold on Linear Ordered Topological Space

关于稳定流形的扰动（续）

On perturbation of stable manifolds ( continued )

树映射的非稳定流形的性质

Some Properties of Unstable Manifolds of Tree Maps

基于稳定流形的方法实现混沌系统的同步

Stable-manifold-based method for realizing chaos synchronization

关于稳定流形的扰动

On perturbation of stable manifolds

本文指出对于一维动力系统，当一周期点不是其不稳定流形的边界点时，其不稳定流形的一个简化形式。

This paper proves a formula which is a simple form of unstable manifolds for periodic points not being on the boundary .

一旦两个非直接耦合的混沌系统的轨迹到达这些稳定流形，其误差系统渐进趋于原点，从而实现两系统的同步。

When the trajectories of two unidirectional-coupled chaotic systems arrive at this manifold , the error dynamics is global asymptotical stable at origin .

半鞍点的稳定流形是系统受限稳定边界的重要部分，并且可以用半鞍点处的等能量面来近似。

The stable manifolds of semi-saddles are significant part of the restricted stability boundary and they can be approximated by equal energy surface of semi-saddles .

这种方法以稳定流形理论为基础，通过设计合适的控制器将混沌系统引至目标轨道，使混沌得以控制和同步。

Based on the stable manifold theory , the chaotic system will be controlled and synchronized if it is guided to the desired target by designing a suitable controller .

该文证明了非线性微分方程组在对应的齐次方程具有指数型二分性、非线性部分满足适当的条件下存在稳定流形和不稳定流形；

In this paper , the author proved that the nonlinear differential equation system exists stable and unstable manifolds if their associated homogenous equations satisfies exponential dichotomy and nonlinear part satisfies certain conditions ;

然后，由停泊轨道向动平衡点目标周期轨道转移，利用该系统的不稳定流形逃逸以实现低能量的星际飞行。

Then the spacecraft transfers from parking orbit to target periodic orbits associated with librations point , and escapes from unstable invariant manifold associated with the system to achieve interplanetary flight with low energy .

为了区分这两种同宿轨道，同时也为本文叙述的方便，我们根据相应的稳定流形和不稳定流形的相对位置，分别为这两种不同类型的同宿轨道命名为大同宿轨道和小同宿轨道。

In order to distinguish these two types of homoclinic orbits and also for the convenience of our statement in this paper , we name these orbits according to the relative position of all the branches of the stable and unstable manifolds .

如果一段具有鞍点特性的相轨迹的起始点从稳定流形的一侧变到另一侧，那么不论系统参数的变化多么细微，其后继轨迹将有完全不同的动态。

No matter how little a parameter changes , if and only if the starting point of a saddle-mode section on the phase plane changes from one side of the stable manifolds to the other side , the dynamics afterwards is entirely different .

具有平行正则平均曲率向量的稳定子流形

On stationary Submanifolds with parallel normalized mean curvature vector

不稳定不变流形的异宿相交可以解释混沌吸引子片结构的突变行为，突变点具有普适的标度，哈密顿映射对于耗散方向的重正化理论可以给出这一普适标度。

The crisis behavior of band structure of chaotic attractors can be explained by heteroclinic crises of unstable invariant manifold . There is a universal scaling law for critical crisis points which can be derived from the dissipative generalization of the Hamiltonian renormalization theory .

边坡稳定分析的流形单元法

Slope Stability Analysis by the Manifold Element Method

文章并没有假定每个节点动态具有公共的平衡解，甚至都没有假定稳定的同步化流形存在。

Neither a common equilibrium for each node nor a stable synchronization manifold is assumed to exist .

计算了与鞍点处的两种稳定和不稳定流形相对应的有界和无界行波解。

The bounded and unbounded traveling wave solutions which correspond to the stable and unstable manifold at the saddle point have been worked out .

该文采用一种新的方法寻找不稳定平衡点的稳定流形，该方法可确定平衡点的稳定流形所满足的偏微分方程。

In this paper a new method is adopted to search for the stable manifolds of unstable equilibrium points so that the stable manifolds of equilibrium points are found easily through partial differential equations .

对于一类两参数平面映射族，给出了一种稳定嵌入在超混沌中不只有稳定流形的不稳定不动点的方法。

For the two-parameter family of planar mapping , a method to stabilize an unstable fixed point without stable manifold embedding in hyperchaos is introduced .

设计控制律使惯性盘倒立摆的部分变量全局渐近稳定，部分变量全局渐近稳定到不变流形。

For an inertia wheel pendulum , a control law is designed to ensure that partial states of an inertia wheel pendulum are globally asymptotically stable , whereas other states are globally asymptotically convergent to an invariant manifold .

应用正规形理论求电力系统在主导不稳定平衡点处的局部稳定和不稳定流形，首先要将电力系统的运动方程的泰勒展开用矩阵表示。

The movement equations of power system should be expressed first in matrix formula-tion before the calculation of stable and unstable manifolds on a controlling unstable equilibrium point in application of normal form theory .

依据非线性动力系统理论，稳定域边界应由其所有不稳定平衡点的稳定流形的并集构成。

According to the theory of nonlinear dynamic system , the stability boundary is the union of the stable manifolds of the equilibrium points on the stability boundary .

仿真结果表明，系统在平衡状态流形上的小振动一般是不稳定的，只在特定初值下存在少量稳定的平衡状态流形。

Discrete numerical simulations show that on most points of the manifold of equilibrium states the system is unstable and that only on some special initial conditions there are few stable equilibrium points .

进而，以该邻域内近似稳定边界上的点作为初值沿时间逆向积分，即采用逆轨迹来近似不稳定平衡点的稳定流形，从而实现了对稳定域的估计。

Hence the stability boundary is approximated by a series of trajectories in reverse time .

根据带约束动力系统稳定域理论，其受限稳定边界由边界上不稳定平衡点、周期轨和半鞍点的稳定流形以及部分可行域边界构成。

According to the stability region theory of constrained dynamic system , the restricted stability boundary is composed of stable manifolds of unstable equilibrium points , periodic orbits and semi-saddles on the boundary , and portions of the boundary of the feasible region .