Resonance dynamics evoked via noise recycling procedure

Abstract

We study the effect of noise recycling on nonequilibrium escape dynamics in a bistable system. For small noise, the non-Markovian problem is reduced to a two-state model with the master equation depending on not only the current state but also the earlier state, based on which we are able to derive the analytical formulas for the switching rate, the autocorrelation function, and the power spectrum density (PSD). Both the theoretical and the numerical results show that, with modulating the time delay in noise recycling, a monotonic PSD may switch to a nonmonotonic one; the amplitude of PSD at resonance frequency exhibits a pronounced maximum at a certain noise level, declaring the onset of stochastic resonance (SR) in the absence of a weak periodic signal. Further, we also demonstrate that the linear response to the external periodic force displays a maximum at a certain level of time delay, displaying the signature of SR.

Numerical study of the influence of recurrent connexions on the signaling in excitable systems: The dynamical effect of noise recycling

“…Similar recycling delay evoked stochastic resonance dynamics are also reported in Sun's work [14], in which the best resonant signal may be obtained at moderate recycling delay level, but further control of the original noise effect are not found in that work. In many other investigations, recycling delay is also reported to be able to adjust the noise effects [5,[7][8][9]13].…”

“…This special kind of noise is also proved to significantly influence the traditional noise effects. It is found to be able to induce stochastic synchronization in a bistable system [5], control the noise enhanced stability in a metastable system [13] and evoke the resonance dynamics [14]. In both the conceptual Brusselator system [7] and the Van der Pol system [9], the recycling time controlled coherence resonance (CR) were reported.…”

“…Recently, their influence through noise recycling, in which a time delayed ingredient of noise is taken into consideration, has receive growing attention [1][2][3][4][5][6][7][8][9][10][11][12][13][14], [15]. In this situation, the noise consists of a primary Gaussian white noise and a secondary same component reinjected after a constant time delay.…”

Modulating resonance behaviors by noise recycling in bistable systems with time delay

“…system have been investigated very recently. 37 The results have demonstrated that resonance behaviors, say coherence and stochastic resonance, can be evoked merely via the noise reinjection procedure. Nevertheless, it is worth mentioning that the particle in the reported researches was specified to trap in a potential without time delay, and the aimed model contained no time delay neither.…”

Dynamical complexity and stochastic resonance in a bistable system with time delay

“…Since its innovative introduction by Benzi and his coworkers [6], SR has been studied extensively both theoretically and experimentally in stochastic bistable systems [7][8][9][10][11][12][13][14][15][16]. Meanwhile, several techniques have been developed or proposed to quantify SR phenomenon, such as signalto-noise ratio (SNR) [9], linear-response theory [10], residence-time distributions [11] and spectral power amplification [12].…”