On the number of limit cycles of planar quadratic vector fields

A study was conducted to investigate the number of limit cycles of planar quadratic vector fields. It was demonstrated that a polynomial vector field was called quadratic when the highest of the degrees of P and Q equaled two. Planar quadratic vector fields had a number of a quadratic vector field surrounding a domain in R2 that contained exactly one singular point of a focus type. It was demonstrated that a focus type singular point was shifted to the origin, while the system was transformed to the Kapteyn normal form.