Bistable sensors based on broken symmetry phenomena: The residence time difference vs. the second harmonic method

A periodically driven noisy bistable system can be used as a sensor of a dc target signal. In the presence of the dc signal the symmetry of the potential energy function that underpins the sensor dynamics can be broken, leading to even harmonics of the driving frequency in the power spectrum. Both the power of the second harmonic and the mean residence time difference can be used for an estimation of the dc signal. In this paper we introduce a method for the power spectrum estimation from the experimental time series. This method can be considered to be an alternative to methods based on the Fourier transform. The presented method is faster for computation than the Fast Fourier Transform, and it allow us to estimate the power contained in peaks (or features) without their mixture with the power spectrum background. Using this method we compute the power of the second harmonic in the response power spectrum and compare the accuracy of the second harmonic method and the mean residence time difference (RTD) via the Shannon mutual information. We find that the RTD, generally, yields better performance in bistable noisy sensors.