Stochastic resonance of a tri-stable system with α stable noise

Liu, Yulei; Liang, Jun; Jiao, Shangbin; Xiao, Nan; Hu, Meng

doi:10.1016/j.cjph.2016.12.010

Cited by 9 publications

(3 citation statements)

References 17 publications

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“…As predicted by the SR scheme (see also [12]), it was shown that the oscillation of the FHN neuron becomes more closely correlated with the subthreshold periodic input current at some optimal level of noise intensity. The stochastic analysis of the FHN neuron and other neuron models has been extensively studied in recent years with various types of noises, multistability, and even how SR can be controlled; see, for example, [13][14][15][16][17][18][19][20][21][22][23].…”

Section: Introductionmentioning

confidence: 99%

Coherent neural oscillations induced by weak synaptic noise

Yamakou

Jost

2018

Nonlinear Dyn

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We analyze the effect of synaptic noise on the dynamics of the FitzHugh-Nagumo (FHN) neuron model. In our deterministic parameter regime, a limit cycle solution cannot emerge through a singular Hopf bifurcation, but such a limit cycle can nevertheless arise as a stochastic effect, as a consequence of weak synaptic noise in a regime of strong timescale separation (ε → 0) between the slow and fast variables of the model. We investigate the mechanism behind this phenomenon, known as self-induced stochastic resonance (SISR) (Muratov et al. in Physica D 210:227-240, 2005), by using multiple-time perturbation techniques and by analyzing the escape mechanism of the random trajectories from the stable manifolds of the model equation. Even though SISR occurs only in the limit as the singular parameter ε → 0, decreasing ε does not increase the coherence of the oscillations in the FHN model, but rather increases the interval of the noise amplitude σ for which coherence occurs. This is in contrast to the dynamical system studied in Mura- 2005). Moreover, the phenomenon is robust under parameter tuning. Numerical simulations exhibit the results predicted by the theoretical analysis. In fact, our analysis together with that in Yamakou and Jost (Weak noise-induced transitions with inhibition and modulation of neural oscillations, 2017) reveals that the FHN model can support different stochastic resonance phenomena. While it had been known (Pikovsky and Kurths in Phys Rev Lett 78:775-778, 1997) that coherence resonance can occur when the slow variable is subjected to noise, we show that, when noise is added to the fast variable, two other types, inverse stochastic resonance and SISR, may emerge in the same weak noise limit and that the transition between these phenomena can be induced by varying a simple parameter.

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Section: Introductionmentioning

confidence: 99%

Coherent neural oscillations induced by weak synaptic noise

Yamakou

Jost

2018

Nonlinear Dyn

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“…When a certain matching relationship is achieved between the signal, the noise, and the multi-stable SR system, the particles can periodically transition between the potential wells, and the output signal of the system is in multiple potentials according to the frequency f of the input signal. The periodic transition is such that the component of the system output x(t) that is of co-frequency with the input signal is enhanced [21][22][23].…”

Section: Multi-stationary Stochastic Resonance Modelmentioning

confidence: 99%

Actuator Weak Fault Diagnosis in Autonomous Underwater Vehicle Based on Tri-Stable Stochastic Resonance

Yang

Guo

et al. 2020

Applied Sciences

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The autonomous underwater vehicle (AUV) is mainly used in the development and exploration of the ocean. As an important module of the AUV, the actuator plays an important role in the normal execution of the AUV. Therefore, the fault diagnosis of the actuator is particularly important. At present, the research on the strong faults, such as the winding of the actuator, has achieved good results, but the research on the weak fault diagnosis is relatively rare. In this paper, the tri-stable stochastic resonance model is analyzed, and the ant colony tri-stable stochastic resonance model is used to diagnose the weak fault. The system accurately diagnoses the fault of the actuator collision and verifies the adaptive tri-stable stochastic resonance system. This model has better diagnostic results than the bi-stable stochastic resonance system.

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“…e problem of weak signal detection using a cascade SR system is studied in [38]. e study of SR in α-stable noise has attracted more and more attention [39][40][41][42][43][44].…”

Section: Introductionmentioning

confidence: 99%

Research on Stochastic Resonance Detection Method for Periodic Signals under Low SNR and α-Stable Noise

Liu³

et al. 2021

Mobile Information Systems

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In Dual Sequence Frequency Hopping (DSFH) communication mode, aiming at improving the detection performance to weak signal under low signal-to-noise ratio (SNR) conditions, stochastic resonance (SR) detection method is proposed. First, the α-stable distribution is used as the impulsive noise model and the influence of α value on the properties of α-stable noise is analyzed. Second, the transmitting and receiving signal model of DSFH communication system is introduced. The SR method is used to detect DSFH signal. In order to analyze the output signal, the fractional Fokker–Planck equation (FFPE) is established, and a new simplified solution method based on sampling decision time is proposed to solve the time-varying fractional differential equation. Base on the theoretical solution of FFPE, a binary hypothesis test statistic is constructed to quantify the signal detection probability and false alarm probability, and the detection performance is analyzed. Finally, simulation experiments verify the theoretical conclusions. The minimum effective SNR for SR detection is obtained, and it is about −20 dB, which provides a theoretical basis for the application of SR in the DSFH communication system.

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Stochastic resonance of a tri-stable system with α stable noise

Cited by 9 publications

References 17 publications

Coherent neural oscillations induced by weak synaptic noise

Coherent neural oscillations induced by weak synaptic noise

Actuator Weak Fault Diagnosis in Autonomous Underwater Vehicle Based on Tri-Stable Stochastic Resonance

Research on Stochastic Resonance Detection Method for Periodic Signals under Low SNR and α-Stable Noise

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