Theory of stochastic resonance for small signals in weakly damped bistable oscillators

Effects of Gaussian colored noise on time evolution of information entropy in a damped harmonic oscillator

“…The relevant Langevin equation of a damped harmonic oscillator driven by Gaussian colored noise is as follows [1][2][3][4][5][6]:…”

“…It is well known that the nature of random force (e.g. noise) may influence the dynamical systems in many aspects, such as stationary probability [7][8][9], escape rate [9,10], noise-induced phase transitions [11,12], stochastic resonance [4,5,[13][14][15] and the time derivative of information entropy [6,[16][17][18][19][20][21][22][23]. The specific nature of the stochastic process may play an important role in the process of equilibration for a given non-equilibrium state of the noise-driven dynamical system.…”

“…The internal dynamics of a force-free harmonic oscillator with additive or multiplicative noise was widely introduced as a model to understand the different phenomena in physics, biology, economics, and so on [1][2][3][4][5][6][7]. However, in most of the models discussed in the literature, the dynamical equations include a deterministic driving force.…”

Optimising threshold levels for information transmission in binary threshold networks: Independent multiplicative noise on each threshold

“…Since first proposed by [3,4], SR has been studied in many nonlinear systems in fields ranging from physics and chemistry to neuroscience and biophysics, for a wide variety of different noise types [5][6][7][8][9][10]. Different Fig.…”

Signal transmission by vibrational resonance in one-way coupled bistable systems

“…This assumption is widely accepted, but it is in contradiction with many known numerical results and stochastic resonance in monostable systems as well. Recently, a rigorous theory of stochastic resonance was developed by Landa et al ͓40,41͔, based on the fact that small noise in stochastic resonance or high-frequency vibration in vibrational resonance may essentially change effective system parameters with respect to slow motions. As a result, both the stochastic and vibrational resonances can be considered in a unique framework.…”