On the cyclicity of a 2-polycycle for quadratic systems
Consider a quadratic system in the plane of the form \[ x'=H_y+\varepsilon P(x,y),\quad y'=-H_x+\varepsilon Q(x,y), \] where \(\epsilon\) is a small parameter and \(H\) is cubic in \((x,y)\). It is assumed that for \(\varepsilon=0\), the system has a heteroclinic loop \(L\) with two hyperbolic saddles belonging to \(\{H=0\}\). The authors give conditions under which the loop \(L\) generates at most two limit cycles (or no cycles) for small \(\varepsilon\).
scientific article; zbMATH DE number 2158598