On The Classification Of The One Dimension DAEs

Systems of differential-algebraic equations (DAEs) have wide application backgrounds, and power systems can be characterized by DAEs. In this paper, The one dimension DAEs with the special algebraic part which is one of y^m+δx^2l-1,y^2k+1+δx^2l and y (yⁿ+δx) ( m , k , l , n∈N+ and n≥2) is studied by using the classification theorem and the norm form theory of the bifurcation problems with trivial solution.Dr. Zhi-Hui Yang researched the classification of the one dimension DAEs with lower codimension ( Codim≤3) under the GT-equivalence in his Doctoral thesis, and this paper not only contains some of systems with lower codimension ( Codim≤3) but also includes a number of systems with codimension greater than 3. For example, the condimension of g (x , y ) is 4 when g ( x , y ) is one of y⁵+δx, y⁵+δxy and y²+δx⁵.This paper will be divided into four chapters.In the first chapter, we briefly introduce the mainly researches and study trends of differential-algebraic equations (DAEs) and we introduce our researches and innovations of this paper.In the second chapter, we introduce some basic concepts and ideas on singularity theory of the bifurcation problems and differential-algebraic equations (DAEs), including GT-equivalent ietc.The main parts are in the third and fouth chapter.In chapter 3, we discuss the classification of the one dimension DAEs with the special algebraic part which is one of y^m +δx^2l-1 and y^2k+1+δx^2l ( m , k ,l∈N₊) under GT-Equivalent.In chapter 4, we make discussion the classification of the one dimension DAEs with the special algebraic part which is y ( yⁿ+δx) ( n∈N₊ and n≥2) under GT-Equivalent in chapter 4 .