Abstract:

The graph classification for a class of quintic algebra curves is carried out by means of the software Mathe-matica and the qualitative analysis method of planar dynamical system.In the classification,first,a planar dynami-cal system corresponding to the quintic algebra curves is constructed.Next,the distributions and properties of sin-gular points are studied.Then,the bifurcation curves are given on the parametric plane.Finally,the graphs of the algebral curves are drawn by using the software Mathematica.Thus,the classification is completed,dividing the graphs into twelve types.

Key words: quintic algebra curve, mathematical model, graph classification, planar dynamical system, qualitative analysis, mathematical software