We focus on the two-dimensional stable manifold of Chen system. Based on the Chen system, a new system with nonlinear control is put forward, which exhibits brand new dynamical phenomena such as the coexistence of heteroclinic orbits with periodic solutions, or two new attractors. The emergence of manifold surface is found by tangential self-intersection. The two-dimensional unstable manifold of saddle-focus tends to another equilibrium solution asymptotically, the underlying heteroclinic bifurcation and the “twins” unstable manifolds are bulit from two saddle-focus respectively.

中文翻译：

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受控陈系统的二维流形

我们专注于 Chen 系统的二维稳定流形。在Chen系统的基础上，提出了一种新的非线性控制系统，它表现出异宿轨道与周期解共存或两个新的吸引子等全新的动力学现象。流形面的出现是通过切向自相交发现的。鞍焦点的二维不稳定流形渐近趋于另一个平衡解，潜在的异宿分岔和“孪生”不稳定流形分别由两个鞍焦点构建而成。