Ogica Global Topoll Classifications For A Class Of Cubic Differential Systems With Star Node

The multinomial differential system has widespread application in ecology domains, life sciences, biochemistry and so on. Many domestic and foreign scholars have made research on it, and particularly, have obtained some good results on global topological structure of some special differential system. Such as square subsystems which have star type point and non-common factor on the right, its limited far singular points only contain the saddle points, the points and half saddle nodes, the system does not have limited cycle, the overall situation phase diagram have only then 17 kinds of different topology. But regarding to three differential system which has star type point, through asks the singular point specifically and judges its topological property is quite complex and difficult extremely, therefore until now there is still no general result.Some properties of cubic differential systems are shown firstly, and then the properties of the tangent vectorfield and its induced vectorfield are also proved. The main method developed by the authors in [1] and [2] are applied to study the topological relationship between the induced vectorfield and the flow of the quadric vectorfield. Finally, the global topological classifications for a class of cubic differential systems with steller node are studied, its topological classifications are also given. It is shown that there exist exactly 26 distinct global phase portrains of the cubic differential systems, and these 26 distinct global phase portrains are also provided.