The doctoral program fund of the Ministry of Education 200806 10000 Project "Some Invariance of Degenerate Systems and Related Functional Equations" The host of the doctoral program fund of the Ministry of Education 2009-2010003 Project "Judgment and Algorithm of Balance and Bifurcation of Complex Vector Fields" The host of the Ministry of Education 2006-2008. The National Natural Science Foundation (10471065438) supported the project "Branches of Higher Degenerate Systems and Iterative Equations Related to Invariant Manifolds" from 2005 to 2007, and the project "Infinite Dimensional Dynamical Systems" supported by the National Outstanding Youth Fund (overseas cooperation category). Foundation (Overseas Cooperation) 2005-2007 Doctoral Foundation of the Ministry of Education 200206 100 Project "Divergence and Invariant Manifold between Center and Degenerate Singularity" 2003-2005 National Natural Science Foundation of the Ministry of Education Project1KLOC-0/07/"Number Equation Problem"