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 these amplitude curves induced by changes of control parameters and the resulting changes of dynamics are studied. In the present paper we investigate changes of dynamics near degenerate singular points of the amplitude profiles.
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