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1·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.

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。

2·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.

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。