Limit cycles of a class of polynomial systems

Abstract

SynopsisWe study the class of polynomial vector fields of the form = αx — y + Pn(x, y), = x + αy + Qn(x, y), where Pn and Qn are homogeneous polynomials of degree n. If we define the functions f(x, y) = xPn(x, y) + yQn(x, y) and g(x, y) = xQn(x, y)−yPn(x, y), we characterise the number of limit cycles for this class when the function g(αg − f) does not change sign.