Generalized stochastic resonance for a fractional harmonic oscillator with bias-signal-modulated trichotomous noise

2018 ◽  
Vol 32 (07) ◽  
pp. 1850072 ◽  
Author(s):  
Lifeng Lin ◽  
Huiqi Wang ◽  
Xipei Huang ◽  
Yongxian Wen
Keyword(s):  
Stochastic Resonance ◽  
Exact Expression ◽  
Order Moment ◽  
Periodic Signal ◽  
External Excitation ◽  
First Order ◽  
Trichotomous Noise ◽  
Output Amplitude ◽  
Fractional Harmonic Oscillator ◽  
Amplitude Amplification

For a fractional linear oscillator subjected to both parametric excitation of trichotomous noise and external excitation of bias-signal-modulated trichotomous noise, the generalized stochastic resonance (GSR) phenomena are investigated in this paper in case the noises are cross-correlative. First, the generalized Shapiro–Loginov formula and generalized fractional Shapiro–Loginov formula are derived. Then, by using the generalized (fractional) Shapiro–Loginov formula and the Laplace transformation technique, the exact expression of the first-order moment of the system’s steady response is obtained. The numerical results show that the evolution of the output amplitude amplification is nonmonotonic with the frequency of periodic signal, the noise parameters, and the fractional order. The GSR phenomena, including single-peak GSR, double-peak GSR and triple-peak GSR, are observed in this system. In addition, the interplay of the multiplicative trichotomous noise, bias-signal-modulated trichotomous noise and memory can induce and diversify the stochastic multi-resonance (SMR) phenomena, and the two kinds of trichotomous noises play opposite roles on the GSR.

Stochastic resonance for a fractional oscillator with random trichotomous mass and random trichotomous frequency

2017 ◽  
Vol 31 (30) ◽  
pp. 1750231 ◽  
Author(s):  
Lifeng Lin ◽  
Huiqi Wang ◽  
Suchuan Zhong
Keyword(s):  
Stochastic Resonance ◽  
Exact Expression ◽  
Order Moment ◽  
Periodic Signal ◽  
Transformation Technique ◽  
First Order ◽  
Fractional Oscillator ◽  
Trichotomous Noise ◽  
Output Amplitude ◽  
Fractional System

The stochastic resonance (SR) phenomena of a linear fractional oscillator with random trichotomous mass and random trichotomous frequency are investigate in this paper. By using the Shapiro–Loginov formula and the Laplace transformation technique, the exact expression of the first-order moment of the system’s steady response is derived. The numerical results demonstrate that the evolution of the output amplitude is nonmonotonic with frequency of the periodic signal, noise parameters and fractional order. The generalized SR (GSR) phenomena, including single GSR (SGSR) and doubly GSR (DGSR), and trebly GSR (TGSR), are detected in this fractional system. Then, the GSR regions in the [Formula: see text] plane are determined through numerical calculations. In addition, the interaction effect of the multiplicative trichotomous noise and memory can diversify the stochastic multiresonance (SMR) phenomena, and induce reverse-resonance phenomena.

scholarly journals The Stochastic Resonance Behaviors of a Generalized Harmonic Oscillator Subject to Multiplicative and Periodically Modulated Noises

2016 ◽  
Vol 2016 ◽  
pp. 1-12 ◽  
Author(s):  
Suchuan Zhong ◽  
Kun Wei ◽  
Lu Zhang ◽  
Hong Ma ◽  
Maokang Luo
Keyword(s):  
Stochastic Resonance ◽  
Internal Noise ◽  
Exact Expression ◽  
Resonance Phenomenon ◽  
Generalized Langevin Equation ◽  
Output Amplitude ◽  
Exact Analytic Expression ◽  
Characteristic Features ◽  
And Control ◽  
Biological Solutions

The stochastic resonance (SR) characteristics of a generalized Langevin linear system driven by a multiplicative noise and a periodically modulated noise are studied (the two noises are correlated). In this paper, we consider a generalized Langevin equation (GLE) driven by an internal noise with long-memory and long-range dependence, such as fractional Gaussian noise (fGn) and Mittag-Leffler noise (M-Ln). Such a model is appropriate to characterize the chemical and biological solutions as well as to some nanotechnological devices. An exact analytic expression of the output amplitude is obtained. Based on it, some characteristic features of stochastic resonance phenomenon are revealed. On the other hand, by the use of the exact expression, we obtain the phase diagram for the resonant behaviors of the output amplitude versus noise intensity under different values of system parameters. These useful results presented in this paper can give the theoretical basis for practical use and control of the SR phenomenon of this mathematical model in future works.

Cooperative mechanism of resonant behaviors in a fluctuating-mass generalized Langevin system with generalized Mittag–Leffler memory kernel

2020 ◽  
Vol 34 (11) ◽  
pp. 2050109
Author(s):  
Lifeng Lin ◽  
Cong Chen ◽  
Huiqi Wang
Keyword(s):  
Stochastic Averaging ◽  
Order Moment ◽  
Generalized Langevin Equation ◽  
Driving Frequency ◽  
Wide Sense ◽  
Memory Kernel ◽  
Dynamical Mechanism ◽  
Output Amplitude ◽  
Bona Fide ◽  
Amplitude Amplification

In this study, we investigate the resonant behaviors in the fluctuating-mass generalized Langevin equation (GLE) with generalized Mittag–Leffler (M–L) memory kernel. By using the stochastic averaging method and Laplace transform, we obtain the exact expression of the first-order moment of system steady response, based on which we analyze the dynamical mechanism of the various non-monotonic phenomena. Based on tbe numerical results, we further discuss the dependence on various parameters systematically and study the interplay and cooperation between the generalized M–L memory kernel and trichotomous noise in terms of output amplitude amplification. The results reveal the coexistence of non-monotonic phenomena in the proposed system, such as bona fide stochastic resonance (SR), conventional SR and wide-sense SR. We even observe the stochastic multi-resonance (SMR) behaviors with five or six peaks in the evolution of output amplitude amplification varying with the driving frequency. It is worth emphasizing that quintuple-peak and sextuple-peak bona fide SR phenomena had never been observed in the previous literatures. Thus, these results will provide more extensive support for manipulating the resonant behaviors through system parameter control in the potential applications.

scholarly journals Stochastic resonance in periodically driven bistable systems subjected to anomalous diffusion

2021 ◽  
Vol 3 (4) ◽  
Author(s):  
F. Naha Nzoupe ◽  
Alain M. Dikandé
Keyword(s):  
Stochastic Resonance ◽  
Signal To Noise Ratio ◽  
Planck Equation ◽  
Relevant Information ◽  
Periodic Signal ◽  
Signal To Noise ◽  
Periodically Driven ◽  
Loop Area ◽  
Bistable Systems ◽  
Noise Ratio

AbstractThe occurrence of stochastic resonance in bistable systems undergoing anomalous diffusions, which arise from density-dependent fluctuations, is investigated with an emphasis on the analytical formulation of the problem as well as a possible analytical derivation of key quantifiers of stochastic resonance. The nonlinear Fokker–Planck equation describing the system dynamics, together with the corresponding Ito–Langevin equation, is formulated. In the linear response regime, analytical expressions of the spectral amplification, of the signal-to-noise ratio and of the hysteresis loop area are derived as quantifiers of stochastic resonance. These quantifiers are found to be strongly dependent on the parameters controlling the type of diffusion; in particular, the peak characterizing the signal-to-noise ratio occurs only in close ranges of parameters. Results introduce the relevant information that, taking into consideration the interactions of anomalous diffusive systems with a periodic signal, can provide a better understanding of the physics of stochastic resonance in bistable systems driven by periodic forces.

scholarly journals An exact expression of positive periodic solution for a first-order singular equation

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Yun Xin ◽  
Xiaoxiao Cui ◽  
Jie Liu
Keyword(s):  
Differential Equation ◽  
Periodic Solution ◽  
Lower Bounds ◽  
Topological Degree ◽  
Order Differential Equation ◽  
Positive Periodic Solution ◽  
Exact Expression ◽  
Upper And Lower Bounds ◽  
Singular Equation ◽  
First Order

Abstract The main purpose of this paper is to obtain an exact expression of the positive periodic solution for a first-order differential equation with attractive and repulsive singularities. Moreover, we prove the existence of at least one positive periodic solution for this equation with an indefinite singularity by applications of topological degree theorem, and give the upper and lower bounds of the positive periodic solution.

Virtual Instrument for Weak Signal Detecting on Monostable Stochastic Resonance

2011 ◽  
Vol 279 ◽  
pp. 361-366
Author(s):  
Quan Yuan ◽  
Yan Shen ◽  
Liang Chen
Keyword(s):  
Power Spectrum ◽  
White Noise ◽  
Stochastic Resonance ◽  
Virtual Instrument ◽  
Stable System ◽  
Periodic Signal ◽  
Nonlinear Phenomenon ◽  
Weak Signal ◽  
Additive White Noise ◽  
Periodic Signals

Stochastic resonance (SR) is a nonlinear phenomenon which can be used to detect weak signal. The theory of SR in a biased mono-stable system driven by multiplicative and additive white noise as well as a weak periodic signal is investigated. The virtual instrument (VI) for weak signal detecting based on this theory is designed with LabVIEW. This instrument can be used to detect weak periodic signals which meets the conditions given and can greatly improved the power spectrum of the weak signal. The results that related to different sets of parameters are given and the features of these results are in accordance with the theory of mono-stable SR. Thus, the application of this theory in the detecting of weak signal is proven to be valid.

Stochastic resonance in an array of integrate-and-fire neurons with threshold

2018 ◽  
Vol 32 (16) ◽  
pp. 1850169 ◽  
Author(s):  
Bingchang Zhou ◽  
Qianqian Qi
Keyword(s):  
Stochastic Resonance ◽  
Additive Noise ◽  
Signal To Noise Ratio ◽  
Array Size ◽  
Periodic Signal ◽  
Signal Parameter ◽  
Input Noise ◽  
Integrate And Fire ◽  
Noisy Input ◽  
Better Than

We investigate the phenomenon of stochastic resonance (SR) in parallel integrate-and-fire neuronal arrays with threshold driven by additive noise or signal-dependent noise (SDN) and a noisy input signal. SR occurs in this system. Whether the system is subject to the additive noise or SDN, the input noise [Formula: see text] weakens the performance of SR but the array size N and signal parameter [Formula: see text] promote the performance of SR. Signal parameter [Formula: see text] promotes the performance of SR for the additive noise, but the peak values of the output signal-to-noise ratio [Formula: see text] first decrease, then increase as [Formula: see text] increases for the SDN. Moreover, when [Formula: see text] tends to infinity, for the SDN, the curve of [Formula: see text] first increases and then decreases, however, for the additive noise, the curve of [Formula: see text] increases to reach a plain. By comparing system performance with the additive noise to one with SDN, we also find that the information transmission of a periodic signal with SDN is significantly better than one with the additive noise in limited array size N.

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