Stochastic resonance in a non-Poissonian dichotomous process: a new analytical approach

Abstract

In this paper we present a new approach to evaluate the average of a function of a stochastic variable in the case of a non-Poissonian dichotomous process. We show that using a two-point correlation function approximation we can explore the asymptotic regime with great precision. We apply our approach to study the phenomenon of stochastic resonance. As an example we consider a resistor–capacitor circuit with a stochastic capacitance C and driven by a periodic voltage. We provide an analytical expression for the average charge in the stationary regime and we show that the amplitude of the average charge, and consequently of the average current, displays the phenomenon of stochastic resonance.

Stochastic Resonance in Simple Electrical Circuits Driven by Quadratic Gaussian Noise

“…These authors assume that the resistance varies dichotomously and they use amplitude of the mean value as an indicator of resonance. A result with no-Poissonian dichotomous noise is provided in [27]. They proposed a system of a resistor-capacitor circuit where noise is put in the capacitance.…”

Effects of a Fluctuating Carrying Capacity on the Generalized Malthus-Verhulst Model

“…Instead, to evaluate the mean value of ( ), we will follow a different approach based on the properties of the correlation function of ( ). In spite of the fact that, usually, the calculations performed using the correlation function are a hard task, sound analytical results can be found (see, e.g., [36]). In this section, we will show a technique that in principle can be applied to other stochastic equations.…”