Tracking stochastic resonance curves using an assisted reference model

Abstract

The optimal noise amplitude for Stochastic Resonance (SR) is located employing an Artificial Neural Network (ANN) reference model with a nonlinear predictive capability. A modified Kalman Filter (KF) was coupled to this reference model in order to compensate for semi-quantitative forecast errors. Three manifestations of stochastic resonance, namely, Periodic Stochastic Resonance (PSR), Aperiodic Stochastic Resonance (ASR), and finally Coherence Resonance (CR) were considered. Using noise amplitude as the control parameter, for the case of PSR and ASR, the cross-correlation curve between the sub-threshold input signal and the system response is tracked. However, using the same parameter the Normalized Variance curve is tracked for the case of CR. The goal of the present work is to track these curves and converge to their respective extremal points. The ANN reference model strategy captures and subsequently predicts the nonlinear features of the model system while the KF compensates for the perturbations inherent to the superimposed noise. This technique, implemented in the FitzHugh-Nagumo model, enabled us to track the resonance curves and eventually locate their optimal (extremal) values. This would yield the optimal value of noise for the three manifestations of the SR phenomena.