Bifurcation of synchronized periodic solutions in systems of coupled oscillators II: Global bifurcation in coupled planar oscillators

We continue the study of a class of differential equations that govern the evolution of indirectly coupled oscillators. In a previous paper we established the existence of synchronized periodic solutions for weak and strong coupling. In this paper we present an example that shows an interesting behavior of the solutions for intermediate coupling strength. We analyze a two-parameter family of branches of periodic solutions and show when a branch has Hopf bifurcation points and/or turning points. We also study the stability of the periodic solutions.