Noise and periodic signal induced stochastic resonance in a Langevin equation with random mass and frequency

Ren, Ruibin; Deng, Ke

doi:10.1016/j.physa.2019.02.030

Cited by 18 publications

(6 citation statements)

References 28 publications

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“…Previous studies on the influence of noise on nerve discharge have achieved rich results. The synergistic effect of noise and system is beneficial to the output of system signals, which is different from people's intuitive understanding of noise [17,18]. Many scholars have studied the effects of white noise, additive noise, phase noise, conductance-based noise and non-Gaussian noise on the random discharge of neurons, suggesting that noise has an important influence on the discharge activity of neurons, so it may participate in the information processing of nervous system, which is helpful to explore the function of randomness in nerve stimulation [19][20][21][22][23][24].…”

Section: Introductionmentioning

confidence: 78%

Effect of potassium channel noise on nerve discharge based on the Chay model

Jiang

Wang

Shang

et al. 2020

THC

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BACKGROUND: The nervous system senses and transmits information through the firing behavior of neurons, and this process is affected by various noises. However, in the previous study of the influence of noise on nerve discharge, the channel of some noise effects is not clear, and the difference from other noises was not examined. OBJECTIVE: To construct ion channel noise which is more biologically significant, and to clarify the basic characteristics of the random firing rhythm of neurons generated by different types of noise acting on ion channels. Method: Based on the dynamics of the ion channel, we constructed ion channel noise. We simulated the nerve discharge based on the Chay model of potassium ion channel noise, and used the nonlinear time series analysis method to measure the certainty and randomness of nerve discharge. RESULTS: In the Chay model with potassium ion noise, the chaotic rhythm defined by the original model could be effectively unified with the random rhythm simulated by the previous random Chay model into a periodic bifurcation process. CONCLUSION: This method clarified the influence of ion channel noise on nerve discharge, better understood the randomness of nerve discharge and provided a more reasonable explanation for the mechanism of nerve discharge.

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Section: Introductionmentioning

confidence: 78%

Effect of potassium channel noise on nerve discharge based on the Chay model

Jiang

Wang

Shang

et al. 2020

THC

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“…( 41) and (( 45)) tells us that the mean field is equal to the average of any single particle's position in some certain threshold. This allows us to study dynamic behaviors of systems among single particles through the the mean field, related to synchronous, mean first passing time (MFPT)(see the definition and related discussion by [29] and [30]), occurring of stochastic resonance, and significant difference on the output gain G for fractional dynamic systems by comparing with traditional dynamic systems with order of the derivative α being or closing the integer 1 in sections 3 and 4 below.…”

Section: Modelling Synchronization Among Mean Fields and General Part...mentioning

confidence: 99%

“…For the numerical simulation, we applied the fractional difference method in [51] (see also [29]), and the simulation parameters are: simulation duration t = 15, time step dt = 0.01, simulation time T = 3000; and also we assume that the initial positions of all the particles in the system obey the normal distribution with mean zero and standard deviation one.…”

Section: The Simulations Of Behaviors For Star-coupled Fractional-ord...mentioning

confidence: 99%

The mechanics of dynamic behaviors for SMEs’ growth by using fractional-order dynamic system approach

Ren

Yuan

2022

J. Finan. Eng.

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The goal of this paper is to establish a general framework for the development of small- or medium-sized enterprises’ (SMEs) growth path by using star-coupled stochastic dynamic system approach. The dynamic behaviors are related to the stochastic resonance (SR) phenomenon subject to multiplicative fluctuation and periodic force which could be interpreted as uncertain environments faced by SMEs (enterprises) during their growth process. The multiplicative noise is modeled as dichotomous noise (uncertainty under the innovation and capital paradigm) and the memory of risk environments is characterized by using fractional kernel function. By using the mathematical derivation, the analytical expressions for the first moment of the steady state response, the stability in the long-time limit in terms of (enterprises) systems’ asymptotic stability is obtained. Theoretic and simulation results show the nonmonotonic dependence between the output gain and the input signal frequency, noise parameters for SMEs dynamic behaviors. Furthermore, the fluctuation noise, the number of related parties (partners) for SMEs, and the fractional-order work together, producing more complex dynamic phenomena compared with the traditional integral-order systems (for enterprises). Finally, theoretical analyses with corresponding numerical simulations results established in this paper would provide a possible fundamental mathematical framework for the study of Schumpeter’s theory on the development for SMEs’ growth under the “innovation and capital paradigm” and related disciplines. In particular, the framework allows us, for the first time, to logically conclude that “in general, the ratio for SMEs’ growth successfully is around less than one-third”, this is actually consistent with what the market has been observing commonly in general.

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“…Therefore, to extend the application of SR, some scholars have studied fractional-order damping systems as alternatives to integer order damping. For example, SR has been observed in fractional-order systems subject to random mass fluctuation and random frequency fluctuation [17][18][19][20][21]. Since many systems are coupled by particles while the above studies only consider a single particle, neglecting the interaction between particles, then the resonant behaviors of coupled fractional systems were studied [22][23][24][25][26][27][28].…”

Section: Introductionmentioning

confidence: 99%

A coupled fractional-order system with fluctuating frequency and its application in bearing fault diagnosis

He¹,

Liu²,

Jiang³

2023

Phys. Scr.

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In this paper, a coupled fractional-order system with fluctuating frequency driven by different periodic signals under various damping strength is investigated. Firstly, based on the Shapiro-Loginov formula and Laplace transform method, the expressions for the output amplitude gain (OAG) of the two subsystems are derived and the resonant behaviors of particles are analyzed. The OAG exhibits various resonance behaviors in response to variations in system parameters, input signals and dichotomous noise, including parameter-induced stochastic resonance, bona-fide resonance and stochastic resonance. Especially, the average behavior of the two output signals is synchronized when two subsystems’ input signals and damping strengths are equal, which is verified in the numerical simulation. Finally, the proposed system is applied to the bearing fault diagnosis to evaluate its engineering application value. The results prove that the system is effective in diagnosing fault signals and has excellent performance.

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Noise and periodic signal induced stochastic resonance in a Langevin equation with random mass and frequency

Cited by 18 publications

References 28 publications

Effect of potassium channel noise on nerve discharge based on the Chay model

Effect of potassium channel noise on nerve discharge based on the Chay model

The mechanics of dynamic behaviors for SMEs’ growth by using fractional-order dynamic system approach

A coupled fractional-order system with fluctuating frequency and its application in bearing fault diagnosis

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