Codimension-2 Bautin bifurcation in the Lü system

In this Letter, rigorous mathematical analysis as well as numerical simulations are used to study the codimension-2 Bautin bifurcation in the chaotic Lü system. Parameter conditions for the Bautin bifurcation are specified and analytical expressions of the bifurcation curves are presented. Consequently, parameter regions for the supercritical and subcritical Hopf bifurcations are also derived. The numerical results agree quite well with the analytical ones.