In this work we discuss new measurement applications of nonlinear micro-resonators that are subject to stochastic forcing in combination with primary periodic excitation. First, we describe how the noise-driven switching of a nonlinear oscillator subjected to harmonic excitation with bistable response can be used as a new type of sensor for measuring parameter changes in the system; we refer to this as the balanced dynamic bridge. For small noise we develop a predictive theory that describes the dynamical behavior of these systems on the oscillator time scale, as well as on the characteristic time scale of the switching. A general theory of activated escape in the presence of a Gaussian noise allows one to compute the switching rates between the two stable states, and the manner in which these rates are related to system parameters. We discuss the high sensitivity of the bridge with respect to changes of system parameters and derive expressions describing the precision of the method and the time required to perform experimental measurements to a given precision. In addition, we discuss application of the dynamical bridge as a sensor of non-Gaussian noise in the presence of additional weak non-Gaussian stochastic forcing. We show how non-Gaussian noise can be detected and estimated by measuring the long-time occupation probability ratio of the bistable states of the system. We conclude our discussion with two examples: they describe non-Gaussian noise estimation in a one-dimensional system and in the nonlinear Mathieu resonator.
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