Uniqueness of limit cycles for a class of cubic systems with two invariant straight lines (Q1958781)

Consider the planar system \[ \dot x= y(1- x^2),\quad\dot y= -x+\delta y+ nx^2+ m xy+ ly^2+ bxy^2 \] having the invariant straight lines \(x\pm 1\). By determining the Lyapunov numbers belonging to the equilibrium at the origin, the authors derive relations implying that (i) the origin is a center, (ii) the number of limit cycles surrounding the origin is \((a)\geq 2\), \((b)= 0\), \((c)\leq 1\).