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Response to parametric modulation near an instability.

The response of a damped anharmonic oscillator, being a model for many systems that undergo a bifurcation, is determined in the presence of small-amplitude parametric modulation of arbitrary dynamics and statistics. Inertia always stabilizes the trivial state and suppresses the growth of the bifurcating solution above the shifted stability threshold. The size of both effects depends on the modulation spectrum. Explicit formulas for threshold, bifurcating solution, and moments are given.