最后，分析了系统的动态性质，给出了经济沿稳定流形收敛于均衡点的条件。
At last, the dynamic system is analyzed, the conditions under which economics converge to equilibrium point are given.
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.
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.
一类是投影点处的轨迹走向服从鞍点规律，且由于投影点位于稳定流形与不稳定流形分割的相平面的上部或下部，故轨迹将沿稳定流形方向到达动态鞍点再沿不稳定流形方向离开该点；
One is the saddle-type structure where the projection point is located either in the up part or the down part of the phase plane, which is divided by both stable and unstable manifolds.
假设期望轨迹由某一稳定外部系统产生，利用中心流形的理论，证明了系统内部动态有界解是存在的。
Supposing that the reference trajectory is generated by a stable system, the bounded solution of non hyperbolic internal dynamics is existed by using center manifold theory.
当失业工人和空闲职位的匹配是有效时，表示经济系统的四维动力系统存在一个稳定的二维流形。
When the match between the unemployed and the vacant positions is efficient, the economic system described by a four-dimensional differential equation system has a stable two-dimensional manifold.
动力学不稳定性模型被推广到有限几何形状的加热面，以解释微电子器件尺寸对池内沸腾换热临界热流形成机理的影响。
The hydrodynamic instability model is spread for finite geometries in order to explain effects of size of microelectronic devices on the mechanism of formation of pool boiling critical heat fluxes.
利用中心流形约化方法证明了霍普夫分歧解的稳定性。
By using the method of centre manifold, the stability of the Hopf bifurcations is also proven.
对于黎曼流形的浸没建立了垂直能量泛函的二阶变分公式，研究强垂直调和映射的稳定性。
The second variation formula of vertical energy functional for a submersion between Riemannian manifolds is calculated with a simple and direct manner.
结果表明，进气门后方具有较大挤气区域的缸盖具有较强的产生缸内斜轴涡流运动的能力，同时也具有较稳定的斜轴涡流形态。
The results indicate that the cylinder head with larger squash area can produce stronger inclined swirl and the outline shape of inclined swirl is steadier.
应用中心流形理论将二元机翼颤振这一四维系统降为二维系统，用后继函数判别法对分叉点的真假中心及稳定性问题进行了分析。
The type and stability of the bifurcation points in the subsequent reduced two dimensional system are analyzed by the method of succeeding function.
证明了拟常曲率流形中二维极小子流形上一个单连通区域为稳定的充分条件。
Sufficient conditions for a simply-connected domain of 2-dimensional minimal submanifold immerged in 2 + p-dimensional manifold of quasi-constant curvature to be stable were proved.
应用实例表明：文中算法稳定、高效，适合于任意复杂的二维流形网格。
Experimental results show that the algorithm is efficient, robust and can be applied to arbitrary complex 2d manifold meshes.
本文摘要叙述有关三维紧致光滑流形上结构稳定的微分同胚的一个特征性定理的证明。
This note takes a sketch of a proof of a characterization theorem for diffeomorphisms oa a compact 3-dimensional smooth manifold to be structurally stable.
然后引入强度折减技术，结合数值流形方法提出了公路路基岩溶顶板稳定性的评价方法。
Then, the evaluating method of the stability of karst roof in roadbed had been established by combining with strength reduction technique and numerical manifold method.
然后引入强度折减技术，结合数值流形方法提出了公路路基岩溶顶板稳定性的评价方法。
Then, the evaluating method of the stability of karst roof in roadbed had been established by combining with strength reduction technique and numerical manifold method.
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