Of A Class Of Plane Quintic Polynomial System, Qualitative Analysis And Global Structure

As in paper [1], Mr. Han Yuliang has discussed the topological structure of the systemsandOn the basis of this case, we mainly discuss the global topological structure of several classes of special fifth polynomial differential systems.Here,we use the tools and methods of paper [1] to study the systems(where and the system(where For the system (1) and (2). because of their only one fmit singular points we use the roots of equation:to discuss all possible infinite singular points, and according to this, we drew out all kinds of phase portraits of them. For the system (3), we use the roots of equationf5(u) = u6 + (h-1)u5+ ku4 + nu3+ mu2+lu + alpha =0 to discuss all the infmitsingular points, and drew out its global phase portraits. Here ,we also obtained theconditions of limit cycles existence or noexistence.