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

Abstract

Dynamics of nonlinear coupled driven oscillators is investigated. Recently, we have demonstrated that the amplitude profiles -- dependence of the amplitude $A$ on frequency $\Omega$ of the driving force, computed by asymptotic methods in implicit form as $F\left( A,\Omega \right) =0$, permit prediction of metamorphoses of dynamics which occur at singular points of the implicit curve $F\left( A,\Omega \right) =0$. 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.