Qualitative Analysis For Several Classes Of Special Fifth Polynomial Differential Systems

In this dissertation,we mainly discuss the qualitative analysis of several classes of special fifth polynomial differential systems with the first and the third critical singular point,that is the system in the first critical casethe system in the third critical caseand the svstemFor the system(1)and (2),each of them can divide into two parts . Discussing each part and using the roots of equations:we can discuss all possible infinite singular points ,in the meanwhile we have discussed the only finite singular point. So we determine all possible phase portraits of the systems.Besides we also give some conditions of the existence and nonexistence of the limit cycle .For the system (3),it is a fifth system with one twenty-first order singular point and one zero eigenvalue ,we have given some conditions of existence and nonexis-tence of the limit cycle.