ON THE NUMBER AND DISTRIBUTIONS OF LIMIT CYCLES OF A PLANAR QUARTIC VECTOR FIELD

In this paper, the number and distributions of limit cycles of a planar quartic vector field are considered. Through perturbation technique and qualitative analysis of differential equation, it is shown that the quartic vector field has 21 limit cycles as parameters satisfy proper conditions. The distributions of limit cycles in the above perturbed planar quartic vector field are also presented.