Bogdanov-Takens系统n次正规形的进一步简化

The nth Regular Form′s Further Simplificatior of the Bogdanov-Takens System

著名的Bogdanov-Takens系统在分岔理论中占有极其重要的地位,许多相关学者都以此作为自己的研究课题之一.作者运用巧妙的数学变换,对Bogdanov-Takens系统n次正规形进行进一步化简计算,得出两种不同类型的简化式,并对每种形式按i,j的不同取值进行分类,所得结果可操作性强,具有公式性,可为以后相关研究工作的开展提供方便.

The famous BogdanovTakens system plays a very important part in the bifurcation theory. Many scholars are interested in the research of it. This thesis successfully simplifies the norder normal form of the BogdanovTakens system by using skillful mathematical method. It presents two kinds of simplified forms and categorizes and each form is based on the value of i and j. The conclusions drawn from that calculation are convenient for scholars to do the further research.