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The interaction of resonances in a weakly nonlinear oscillator with a quasiperiodic excitation.

Conditions for chaos onset due to the interaction of resonances in a weakly nonlinear oscillator with a quasiperiodic excitation are investigated. The focus is made on the interaction of the 1:1 resonance with that of 1:m, where m is an arbitrary integer number. Analytical conditions of the chaos arising are obtained through the combined application of the averaging procedure and Melnikov's technique. The comparison study of these conditions with those following from standard Chirikov's approach is provided. (c) 1997 American Institute of Physics.