levy noise
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2022 ◽  
Vol 9 ◽  
pp. 213-280
Quentin Berger ◽  
Hubert Lacoin

2022 ◽  
Hanwen Zhang ◽  
Zhen Qin ◽  
Yichao Zhang ◽  
Dajiang Chen ◽  
Ji Gen ◽  

Abstract The Gaussian noise model has been chosen for underwater information sensing tasks under substantial interference for most of the research at present. However, it often contains a strong impact and does not conform to the Gaussian distribution. In this paper, a practical underwater information sensing system is proposed based on intermittent chaos under the background of Lévy noise. In this system, a novel Lévy noise model is presented to describe the underwater natural environment interference and estimate its parameters, which can better describe the impact characteristics of the underwater environment. Then an underwater environment sensing method of dual-coupled intermittent chaotic Duffing oscillator is improved by using the variable step-size method and scale transformation. The simulation results show that the method can sense weak signals and estimate their frequencies under the background of strong Lévy noise, and the estimation error is as low as 0.03%. Compared with the intermittent chaos of the single Duffing oscillator and the intermittent chaotic Duffing of double coupling, the minimum SNR ratio threshold has been reduced by 11.5dB and 6.9dB, respectively, and the computational cost significantly reduced, and the sensing efficiency is significantly improved.

2021 ◽  
Vol 31 (16) ◽  
Wenting Zhang ◽  
Wei Xu ◽  
Qin Guo ◽  
Hongxia Zhang

The birhythmic oscillation is of great significance in biology and engineering, and this paper presents a bifurcation analysis in a time-delayed birhythmic oscillator containing fractional derivative and Lévy noise. The numerical method is used to explore the influence of various parameters on the bifurcation of the birhythmic system, and the role of fractional derivative and Lévy noise in inducing or inhibiting birhythmicity in a time-delayed birhythmic biological system is examined in this work. First, we use a numerical method to calculate the fractional derivative, which has a fast calculation speed. Then the McCulloch algorithm is employed to generate Lévy random numbers. Finally, the stationary probability density function graph of the amplitude is obtained by Monte Carlo simulation. The results show that the fractional damping and Lévy noise can effectively control the characteristics of the birhythmic oscillator, and the change of the parameters (except the skewness parameter) can cause the system bifurcation. In addition, this article further discusses the interaction of fractional derivative and time delay in a birhythmic system with Lévy noise, proving that adjusting parameters of time delay can lead to abundant bifurcations. Our research may help to further explore the bifurcation phenomenon of birhythmic biological system, and has a practical significance.

2021 ◽  
Tadeusz Kulczycki ◽  
Alexei Kulik ◽  
Michał Ryznar

Marius E. Yamakou ◽  
Tat Dat Tran

AbstractAll previous studies on self-induced stochastic resonance (SISR) in neural systems have only considered the idealized Gaussian white noise. Moreover, these studies have ignored one electrophysiological aspect of the nerve cell: its memristive properties. In this paper, first, we show that in the excitable regime, the asymptotic matching of the deterministic timescale and mean escape timescale of an $$\alpha $$ α -stable Lévy process (with value increasing as a power $$\sigma ^{-\alpha }$$ σ - α of the noise amplitude $$\sigma $$ σ , unlike the mean escape timescale of a Gaussian process which increases as in Kramers’ law) can also induce a strong SISR. In addition, it is shown that the degree of SISR induced by Lévy noise is not always higher than that of Gaussian noise. Second, we show that, for both types of noises, the two memristive properties of the neuron have opposite effects on the degree of SISR: the stronger the feedback gain parameter that controls the modulation of the membrane potential with the magnetic flux and the weaker the feedback gain parameter that controls the saturation of the magnetic flux, the higher the degree of SISR. Finally, we show that, for both types of noises, the degree of SISR in the memristive neuron is always higher than in the non-memristive neuron. Our results could guide hardware implementations of neuromorphic silicon circuits operating in noisy regimes.

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