Abstract: We study dynamics of two coupled periodically driven oscillators. Im- portant example of such a system is a dynamic vibration absorber which consists of a small mass attached to the primary vibrating system of a large mass. Periodic solutions of the approximate effective equation derived in our earlier work are determined within the Krylov–Bogoliubov–Mitropolsky (KBM) approach used to compute the amplitude profiles A(Ω). Depen- dence of the amplitude A of nonlinear resonances on the frequency Ω is much more complicated than in the case of one Duffing oscillator and hence new nonlinear phenomena are possible. In the present paper we study metamorphoses of the function A(Ω) induced by changes of the control parameters near a singular point of this function. It follows that dynamics can be controlled in the neighbourhood of a singular point.
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