A Class Of Planar Polynomial Differential Systems Qualitative Analysis

In this paper, we consider a ceitain l)lane qualtl( ~ystern with the stellar node 4 x ?a40x4 + aa1x3y ?a22x2y2 + a13xy3 ?ao4y ?y + b4ox4 + b3ix3y + b22x2y2 + b13sry3 + b04y4 By analyzing the number of the nodes and the roots of the equation (I) and the tegions of type I桾V, WC discuss its global to [)ol ogt (al st riictu re a.I 1 d give the, r corresponding condition and soirie exa 111 pies. I b40 + (b31 ?a40)u + (b22 ?a31 )u2 + (b13 ?a22)u3 + (b04 ?a13)u4 ? 0 Altogether, the system has six points at most. We get six cases. It may have eight, twenty, thirty-three, ninteen, eleven, three different kinds of global structure, respec- tively. Then, we give all the global phase diagrams.