Memory-enhanced energetic stability for a fractional oscillator with fluctuating frequency

Abstract

The long-time limit behavior of the variance and the correlation function for the output signal of a fractional oscillator with fluctuating eigenfrequency subjected to a periodic force is considered. The influence of a fluctuating environment is modeled by a multiplicative white noise and by an additive noise with a zero mean. The viscoelastic-type friction kernel with memory is assumed as a power-law function of time. The exact expressions of stochastic resonance (SR) characteristics such as variance and signal-to-noise ratio (SNR) have been calculated. It is shown that at intermediate values of the memory exponent the energetic stability of the oscillator is significantly enhanced in comparison with the cases of strong and low memory. A multiresonancelike behavior of the variance and SNR as functions of the memory exponent is observed and a connection between this effect and the memory-induced enhancement of energetic stability is established. The effect of memory-induced energetic stability encountered in case the harmonic potential is absent, is also discussed.

Friction-induced Resonance in a Noisy Fractional Oscillator

“…This is quite surprising in view of the fact that the importance of multiplicative fluctuations and viscoelasticity for biological systems, e.g., living cells, has been well recognized [17,18]. Thus motivated, the authors of [10,19] have recently considered fractional oscillators with fluctuating eigenfrequency subjected to an external periodic force and an additive noise. These models demonstrate that an interplay of noises and memory can generate a variety of cooperative effects, such as memory-enhanced energetic stability, stochastic resonance (SR) versus noise parameters, as well as frictioninduced resonance.…”

“…The present work is a follow-up of a previous investigation of the fractional oscillator with multiplicative white noise [10]. The main purpose of this paper is to demonstrate, partially on the bases of the exact expressions of SR characteristics found in [10], that in certain parameter regions the output spectral amplification and signal-tonoise ratio (SNR) exhibit a resonance-like nonmonotonic behavior versus the friction coefficient.…”

“…One of the objects of special attention in this context is the noise-driven fractional oscillator. The dynamical equation for such an oscillator is obtained by replacing the usual friction term in the dynamical equation for a harmonic oscillator by a generalized friction term with a power-law type memory [6]- [10]. The main advantage of this equation is that it provides a physically transparent and mathematically tractable description of the stochastic dynamics observable in systems with slow relaxation processes and with anomalously slow diffusion.…”

“…The main purpose of this paper is to demonstrate, partially on the bases of the exact expressions of SR characteristics found in [10], that in certain parameter regions the output spectral amplification and signal-tonoise ratio (SNR) exhibit a resonance-like nonmonotonic behavior versus the friction coefficient. Furthermore, we establish the sufficient conditions for the occurrence of friction-induced multiresonance of SNR.…”

Interspike interval distribution of a resonate-and-fire neuron model driven by Mittag-Leffler noise

“…One of the possibilities for modeling such processes can be formulated in the framework of the generalized Langevin equation (GLE) [22,23]. The dynamical equation for such systems is in most cases obtained by replacing the usual friction term in the Langevin equation by a generalized friction term with a power-law memory [22,23,24]. Physically such a friction term has, due to the fluctuation-dissipation theorem, its origin in a nonohmic thermal bath whose influence on the dynamical system is described with a power-law correlated additive noise in the GLE [22].…”