Simulation of Circuits Demonstrating Stochastic Resonance

In certain dynamical systems, the addition of noise can assist the detection of a signal and not degrade it as normally expected. This is possible via a phenomenon termed stochastic resonance (SR) . The response of a nonlinear system to a sub-threshold periodic input signal is optimal for some non-zero value of noise intensity. Using the signal-to-noise ratio (SNR) we can characterise SR — as the noise increases the SNR rises sharply, which is followed by a gradual decrease. We investigate the SR phenomenon in several circuits and numerical simulations. In particular, the effect that the system linearity has on the amount of gain introduced by SR and the effect of varying the input signal strength. We demonstrate, for a thresholding system, as much as a 20 dB improvement in SNR, which may be increased by further investigation. Although SR occurs in many disciplines, the sinusoidal signal itself is not information bearing. To greatly enhance the practical applications of SR, we require operation with an aperiodic broadband signal. Hence, we introduce aperiodic stochastic resonance (ASR) where noise can enhance the response of a nonlinear system to a weak aperiodic signal. As the input signal is aperiodic, an alternate quantitative measure is required rather than the SNR used with periodic signals. We can characterise ASR by the use of cross-correlation-based measures. Using this measure, the ASR in a simple threshold system and in a FitzHugh-Nagumo neuronal model are compared using numerical simulations. Using both weak periodic and aperiodic signals we show that the response of a nonlinear system is enhanced, regardless of the signal.