Metamorphoses of amplitude curves in a system of coupled oscillators: the case of degenerate singular points

We study dynamics of two coupled periodically driven oscillators. The internal motion is separated off exactly to yield a nonlinear
fourth-order equation describing inner dynamics. Periodic steady-state solutions of the fourth-order equation are determined within the
Krylov-Bogoliubov-Mitropolsky (KBM) approach and the corresponding amplitude profiles are computed.
Metamorphoses of the corresponding amplitude curves induced by changes of control parameters and the corresponding changes
of dynamics are studied. In the present paper we investigate changes of dynamics near degenerate singular points of the amplitude
profiles.