Stochastic resonance (SR) is numerically analyzed by the method of the stochastic energetics that enable us to analyze the energetics of non-equilibrium processes described by the Langevin equations. The work done by the external agent which drives the potential to fluctuate periodically is...

We studied the motion of an underdamped Brownian particle in a periodic potential subject to a harmonic excitation and a colored noise. The average input energy per period and the phase lag are calculated to quantify the phenomenon of stochastic resonance (SR). The numerical results show that...

A relation giving a minimum for the irreversible work in quasi-equilibrium processes was derived by Sekimoto et al. [K. Sekimoto, S. Sasa, J. Phys. Soc. Japan 66 (1997) 3326] in the framework of stochastic energetics. This relation can also be written as a type of “uncertainty principle” in...

We propose an energetic interpretation of stochastic processes described by Langevin equations with non-uniform temperature. In order to avoid Itô–Stratonovich dilemma, we start with a Kramers equation, and derive a Fokker–Planck equation by the renormalization group method. We give a...

The subject of the present paper is a simplified model for a symmetric bistable system with memory or delay, the reference model, which in the presence of noise exhibits a phenomenon similar to what is known as stochastic resonance. The reference model is given by a one dimensional parametrized...

We have analyzed the interplay between noise and periodic modulations in a mean field model of a neural excitable medium. To this purpose, we have considered two types of modulations; namely, variations of the resistance and oscillations of the threshold. In both cases, stochastic resonance is...

Suppose a two-dimensional dynamical system has a stable attractor that is surrounded by an unstable limit cycle. If the system is additively perturbed by white noise, the rate of escape through the limit cycle will fall off exponentially as the noise strength. The presence of this slowly...

We present simple classical dynamical models to illustrate the idea of introducing a stochasticity with non-locality into the time variable. For stochasticity in time, these models include noise in the time variable but not in the “space” variable, which is opposite to the normal description...

Stochastic resonance is investigated in a system of threshold elements located at nodes and coupled along edges of a Barabási–Albert network, driven by a common subthreshold periodic signal and independent noises. Array-enhanced stochastic resonance is observed, i.e., increase of the spectral...

The phenomenon of stochastic resonance has recently been found in many systems. Despite the pre-conception of a destructive role of noise, its constructive role has been recognised, in particular in amplification of weak external signals, thereby facilitating signal detection and transduction in...