Summary: The authors discuss systems of the form \[ \begin{aligned}\dot x&=\lambda x+y+ p(x,y)+ xf(x,y),\\ \dot y&=-x +\lambda y+q(x,y) +yf(x,y), \end{aligned} \] where \(p,q\) and \(f\) are all homogeneous quadratic polynomials; coordinates are chosen so that the linear part is in canonical form. Systems of this form are used as examples in various contexts and the purpose of this paper is to present a unified account of the results obtained over the years.