稳定流形(stable manifold)是微分动力系统的基本概念，它是微分动力系统研究的重要内容。稳定与不稳定流形是动力系统的不动点或周期轨附近当时间趋于无穷时会趋于该轨的点的集合。按时间趋于正无穷或负无穷可分别得到稳定流形和不稳定流形。稳定与不稳定流形的概念可以从不动点或周期轨推广到任意一点，从而得到双曲集的重要概念。
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.
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