Collective stochastic resonance behavior in the globally coupled fractional oscillator

Zhong, Shun; Lv, Wangyong; Ma, Hong; Zhang, Lu

doi:10.1007/s11071-018-4401-0

Cited by 21 publications

(7 citation statements)

References 41 publications

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“…Now we get the following closed differential equations with four unknown variables (based on equations ( 9) and ( 12)) : Subsequently, the Laplace transform method [36] is applied to solve the equations (13 ), and Y i (s) represents the Laplace transform result of y i :…”

Section: Analytical Solution Of Steady-state Response Output Of Modelmentioning

confidence: 99%

Stochastic resonance of double fractional-order coupled oscillator with mass and damping fluctuations

Ren¹,

Xia²,

Zhe-Zheng³

et al. 2022

Phys. Scr.

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In this study, the stochastic resonance phenomenon of a coupled double fractional-order harmonic oscillator with mass and damping fluctuation is investigated. Firstly, the Shapiro-Loginov formula and Laplace transform are used to obtain the analytical expression of the output amplitude gain of the system output. On this basis, aiming at the key factors involved in the model, including the coupling structure, fractional system, random fluctuation and external periodic force, the influence of coupling coefficient, double fractional order and driving frequency on the output amplitude gain (OAG) are analyzed, and reasonable physical explanations are provided. Secondly, numerical simulations are carried out to verify the accuracy of the theoretical solutions. The simulation results show that under certain conditions, the OAG of the system can appear stochastic resonance phenomenon with the above parameters, especially: 1) The OAG with the change of external drive frequency appears double peak, single peak and single valley stochastic resonance phenomenon, which does not appear under the same external disturbance with integer order and uncoupled conditions; 2) The order of double fractional derivative significantly affects the variation trend of OAG; 3) The coupling coefficient is not sensitive to the OAG.

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Section: Analytical Solution Of Steady-state Response Output Of Modelmentioning

confidence: 99%

Stochastic resonance of double fractional-order coupled oscillator with mass and damping fluctuations

Ren¹,

Xia²,

Zhe-Zheng³

et al. 2022

Phys. Scr.

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show abstract

“…A coupled system refers to a system consisting of finite (or infinite) local (or global) coupled elements [18], such as complex networks, where the particles are interconnected, making the coupled model crucial for accurately describing real-world problems. Consequently, there is a growing interest among scholars in exploring SR within coupled systems [19][20][21][22][23][24][25]. For instance, Vishwamittar et al [19] delved into the study of collective resonant behavior in two coupled fractional oscillators subjected to quadratic asymmetric dichotomous noise.…”

Section: Introductionmentioning

confidence: 99%

Time-Delay Effects on the Collective Resonant Behavior in Two Coupled Fractional Oscillators with Frequency Fluctuations

He,

Wang,

Lin

2024

Fractal Fract

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In this study, we propose coupled time-delayed fractional oscillators with dichotomous fluctuating frequencies and investigate the collective resonant behavior. Firstly, we obtain the condition of complete synchronization between the average behavior of the two oscillators. Subsequently, we derive the precise analytical expression of the output amplitude gain. Based on the analytical results, we observe the collective resonant behavior of the coupled time-delayed system and further study its dependence on various system parameters. The observed results underscore that the coupling strength, fractional order, and time delay play significant roles in controlling the collective resonant behavior by facilitating the occurrence and optimizing the intensity. Finally, numerical simulations are also conducted and verify the accuracy of the analytical results.

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“…Among three ingredients for activating SR including noise, nonlinear systems and weak useful signals, nonlinear systems are crucial ingredients for extracting weak useful signals and moreover can harvest the energy of noise located at the whole frequency band of a noisy signal to enhance or amplify a weak useful signal. For this purpose, most of scholars pay attention to exploring the behaviors of SR in novel nonlinear systems from bistable [6] to multistable ones [7][8][9], from overdamped [10] and underdamped [11] to fractional-order [12] ones, and even from cascaded [13] and coupled [14,15] to time-delayed feedback [16] ones and biological systems [17,18]. Because the bistable system is most classical among them, it has been investigated, such as classical bistable potential overdamped systems, noisy confined bistable potential overdamped systems [19], asymmetric bistable potential overdamped systems [20], classical bistable potential underdamped systems, noisy bistable potential fractional-order systems [21] and E-exponential potential underdamped systems [22,23].…”

Section: Introductionmentioning

confidence: 99%

Harmonic-Gaussian double-well potential stochastic resonance with its application to enhance weak fault characteristics of machinery

et al. 2023

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Although noise is ubiquitous and unwanted in detecting weak signals, the phenomenon of stochastic resonance (SR) is beneficial for enhancing weak signals embedded in signals with strong background noise. Taking into account that nonlinear systems are crucial ingredients to activate the SR, here we investigate the SR in the cases of overdamped and underdamped harmonic-Gaussian double-well potential systems subjected to noise and a periodic force. We derive and measure the analytic expression of the output signal-to-noise ratio (SNR) and the steady-state probability density (SPD) function under approximate adiabatic conditions. When the harmonic-Gaussian double-well potential loses its stability, we can observe the antiresonance phenomenon, whereas adding the damped factor into the overdamped system can change the stability of the harmonic-Gaussian double-well potential, resulting that the antiresonance behavior disappears in the underdamped system. Then, we use the overdamped and underdamped harmonic-Gaussian double-well potential

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Collective stochastic resonance behavior in the globally coupled fractional oscillator

Cited by 21 publications

References 41 publications

Stochastic resonance of double fractional-order coupled oscillator with mass and damping fluctuations

Stochastic resonance of double fractional-order coupled oscillator with mass and damping fluctuations

Time-Delay Effects on the Collective Resonant Behavior in Two Coupled Fractional Oscillators with Frequency Fluctuations

Harmonic-Gaussian double-well potential stochastic resonance with its application to enhance weak fault characteristics of machinery

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