Parametric oscillation conditions for periodically timevariant system and stability failure of periodic motion of nonlinear dynamic system are derived within the monofrequency approximation. Graphical illustration and physically based explanation for oscillation conditions are given. Conditions for two-frequency combined oscillation of s u m and difference resonance phenomenon and high frequency synchronization are obtained. A problem of nonlinear system robust control avoiding one-frequency parametric resonances is set up.

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