Analysis of global bifurcation for a class of systems of degree five
Consider the two-dimensional system \[ dx/dt= y,\quad dy/dt= -x-(x^2- a)(1+ y^2)y,\tag{\(*\)} \] where \(a\) is a parameter. The authors give a complete bifurcation analysis of \((*)\) and prove that \((*)\) has a unique stable limit cycle for some parameter interval which is generated by a Hopf and a separatrix loop bifurcation correspondingly.
scientific article; zbMATH DE number 1218604