Effective equation for two coupled oscillators: towards a global view of metamorphoses of the amplitude profiles

Dynamics of nonlinear coupled driven oscillators is investigated. Recently, we have demonstrated that the amplitude profiles – dependence of the amplitude $A$ on frequency $\mathrm{\Omega }$ of the driving force, computed by asymptotic methods in implicit form as $F(A,\mathrm{\Omega })=0$, permit prediction of metamorphoses of dynamics which occur at singular points of the implicit curve $F(A,\mathrm{\Omega })=0$. In the present study we strive at a global view of singular points of the amplitude profiles computing bifurcation sets, i.e. sets containing all points in the parameter space for which the amplitude profile has a singular point.