Abstract
We study dynamics of two coupled periodically driven oscillators in general case. Periodic steady-state solutions of the system of two equations are determined within the Krylov–Bogoliubov–Mitropolsky approach. The corresponding amplitude profiles, A(ω),B(ω), which are given by two implicit equations, F(A,B,ω)=0,G(A,B,ω)=0, where ω is frequency of the driving force, are computed. These two equations, each describing a surface, define a 3D curve-intersection of these surfaces. In the present paper we carry out preliminary investigation of metamorphoses of this curve, induced by changes of control parameters. The corresponding changes of dynamics near singular points of the curve are studied.
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