Colored Levy Noise Induced Stochastic Dynamics in a Tri-Stable Hybrid Energy Harvester

2021 ◽  
Author(s):  
Yanxia Zhang ◽  
Yanfei Jin
Keyword(s):  
Energy Harvester ◽  
Stochastic Dynamics ◽  
Signal To Noise Ratio ◽  
Lévy Noise ◽  
Largest Lyapunov Exponent ◽  
Vibration Energy Harvester ◽  
Hybrid Energy ◽  
Brownian Noise ◽  
The Mean ◽  
Levy Noise

Abstract The piezoelectric and electromagnetic hybrid vibration energy harvester (HVEH) has proven to be a favorable option to deal with the low power generation issue and overcome the drawbacks of each individual transduction mechanism. Besides, colored Lévy noise consisting of small perturbations, large jumps and correlation time turns out to be a relatively suitable tool for describing the complex environments. For the purpose of enhancing the harvesting performance of HVEH, the stochastic dynamics induced by colored Lévy noise in a tri-stable HVEH is mainly investigated in this paper. The stationary probability density, the largest Lyapunov exponent, the signal-to-noise ratio and the mean harvested power are calculated to explore the stochastic dynamics of system, such as the stochastic response, the stochastic stability, the stochastic resonance (SR) and the energy harvesting performance. Results show that the colored Lévy noise can induce stochastic P-bifurcation, D-bifurcation and SR phenomenon. In particular, the comparisons between colored Lévy noise and colored Brownian noise in dynamics and harvesting performance are also discussed in detail. It is found that the colored Lévy noise can make a greater contribution than colored Brownian noise in the effective voltage and help to improve the mean harvested power through the SR effect.

STOCHASTIC PROPERTIES OF TUMOR GROWTH DRIVEN BY WHITE LÉVY NOISE

2012 ◽  
Vol 26 (23) ◽  
pp. 1250149 ◽  
Author(s):  
LILI JIANG ◽  
XIAOQIN LUO ◽  
DAN WU ◽  
SHIQUN ZHU
Keyword(s):  
Tumor Growth ◽  
First Passage Time ◽  
Dynamical Behavior ◽  
Gaussian White Noise ◽  
Passage Time ◽  
Lévy Noise ◽  
Mean First Passage Time ◽  
First Passage ◽  
The Mean ◽  
Levy Noise

The dynamical behavior of tumor growth model driven by Lévy noise terms is investigated. For α = 2 and β = 0, the process driven by white Lévy noise approach to the standard Gaussian white noise can be viewed in the analysis of the steady-state probability distribution and the mean first-passage time. When β → 0, the index α would increase the mean first-passage time as scale σ < 0 and shorten the mean first-passage time as scale σ > 0. A nonzero β parameter induces α to decrease the mean first-passage time. Thus analyzing the initial situation of tumor is very important to obtain more therapy time.

Lévy Noise-Induced Effects in Underdamped Asymmetric Bistable System

2019 ◽  
Vol 19 (01) ◽  
pp. 2050007
Author(s):  
Yongfeng Guo ◽  
Fang Wei ◽  
Linjie Wang
Keyword(s):  
Numerical Solutions ◽  
Signal To Noise Ratio ◽  
Stability Index ◽  
Signal Amplitude ◽  
Noise Signal ◽  
Bistable System ◽  
Index Formula ◽  
Lévy Noise ◽  
Steady State Probability ◽  
Levy Noise

This paper aims to explore the Lévy noise-induced effects in underdamped asymmetric bistable system. Lévy noise is generated by Janicki–Weron algorithm which is different from the usual Gaussian noise. The numerical solutions of system equation are obtained by the fourth-order stochastic Runge–Kutta algorithm. Then the quasi-steady-state probability density (QSPD) is obtained by solving the equation of system, and the stochastic resonance (SR) is determined by the classical measure of signal-to-noise ratio (SNR). The influence of various parameters of the Lévy noise and the system parameters on QSPD and SNR is discussed. Noise-induced transitions occur by varying the parameters of the Lévy noise and the driven system. Moreover, within certain limits, the larger value of the stability index [Formula: see text] of Lévy noise, signal amplitude [Formula: see text], and the absolute values of asymmetric parameter [Formula: see text] can give rise to the SR phenomenon. On the contrary, the larger values of skewness parameters [Formula: see text] of Lévy noise and damping parameter [Formula: see text] further weaken the occurrence of the SR phenomenon in the given system.

Bifurcation Analysis of an Energy Harvesting System with Fractional Order Damping Driven by Colored Noise

2021 ◽  
Vol 31 (15) ◽  
Author(s):  
Yong-Ge Yang ◽  
Ya-Hui Sun ◽  
Wei Xu
Keyword(s):  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Fractional Order ◽  
Colored Noise ◽  
Energy Harvester ◽  
Advanced Materials ◽  
Vibration Energy ◽  
Vibration Energy Harvester ◽  
The Mean

Vibration energy harvester, which can convert mechanical energy to electrical energy so as to achieve self-powered micro-electromechanical systems (MEMS), has received extensive attention. In order to improve the efficiency of vibration energy harvesters, many approaches, including the use of advanced materials and stochastic loading, have been adopted. As the viscoelastic property of advanced materials can be well described by fractional calculus, it is necessary to further discuss the dynamical behavior of the fractional-order vibration energy harvester. In this paper, the stochastic P-bifurcation of a fractional-order vibration energy harvester subjected to colored noise is investigated. Variable transformation is utilized to obtain the approximate equivalent system. Probability density function for the amplitude of the system response is derived via the stochastic averaging method. Numerical results are presented to verify the proposed method. Critical conditions for stochastic P-bifurcation are provided according to the change of the peak number for the probability density function. Then bifurcation diagrams in the parameter planes are analyzed. The influences of parameters in the system on the mean harvested power are discussed. It is found that the mean harvested power increases with the enhancement of the noise intensity, while it decreases with the increase of the fractional order and the correlation time.

Dynamic characteristics in two-dimensional FitzHugh–Nagumo neural system driven by Lévy noise

2019 ◽  
Vol 33 (28) ◽  
pp. 1950345 ◽  
Author(s):  
Linjie Wang ◽  
Yongfeng Guo ◽  
Fang Wei ◽  
Jianguo Tan
Keyword(s):  
Steady State ◽  
Signal To Noise Ratio ◽  
Neural System ◽  
Lévy Noise ◽  
Stationary Probability ◽  
Two Dimensional ◽  
Signal To Noise ◽  
Neuron System ◽  
Runge Kutta Method ◽  
Levy Noise

In this paper, the steady state characteristics and stochastic resonance (SR) in two-dimensional FitzHugh–Nagumo (FHN) neuron system driven by Lévy noise are studied. The system is simulated by Janicki–Weron algorithm and fourth-order Runge–Kutta method, and the steady state characteristics of the system are analyzed by stationary probability density (SPD) functions. Then, the SR is determined by the classical measure of signal-to-noise ratio (SNR). Through numerical simulation, it is found that the Lévy noise can induce the transition of the system. In addition, the effects of different parameters on the SR are analyzed by SNR.

scholarly journals Strong solutions for the stochastic 3D LANS-α model driven by non-Gaussian Lévy noise

2015 ◽  
Vol 15 (02) ◽  
pp. 1550011
Author(s):  
Gabriel Deugoué ◽  
Mamadou Sango
Keyword(s):  
Strong Solution ◽  
Strong Solutions ◽  
Lévy Noise ◽  
Mean Square ◽  
Stability Of Solutions ◽  
Model Driven ◽  
The Mean ◽  
The Stability ◽  
Non Gaussian ◽  
Levy Noise

We establish the existence, uniqueness and approximation of the strong solutions for the stochastic 3D LANS-α model driven by a non-Gaussian Lévy noise. Moreover, we also study the stability of solutions. In particular, we prove that under some conditions on the forcing terms, the strong solution converges exponentially in the mean square and almost surely exponentially to the stationary solution.

scholarly journals Lévy Noise-induced Self-induced Stochastic Resonance in a Memristive Neuron

2021 ◽  
Author(s):  
Marius E. Yamakou ◽  
Tat Dat Tran
Keyword(s):  
Magnetic Flux ◽  
Stochastic Resonance ◽  
Gaussian White Noise ◽  
Scaling Limit ◽  
Lévy Noise ◽  
Feedback Gain ◽  
Neuromorphic Circuits ◽  
Gain Parameter ◽  
The Mean ◽  
Levy Noise

Abstract Self-induced stochastic resonance (SISR) is a subtle resonance mechanism requiring a nontrivial scaling limit between the stochastic and the deterministic timescales of an excitable system, leading to the emergence of a limit cycle behavior which is absent without noise. All previous studies on 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 mean escape timescale of an α-stable Lévy process (with value increasing as a power σ-α of the noise amplitude σ, unlike the mean escape timescale of a Gaussian process with the value increasing as in Kramers' law) and the deterministic timescale (controlled by the singular parameter) 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 find applications in designing neuromorphic circuits operating in noisy regimes.

First-passage behavior of under-damped asymmetric bistable system driven by Lévy noise

2020 ◽  
Vol 34 (31) ◽  
pp. 2050348
Author(s):  
Xiuxian Yu ◽  
Yongfeng Guo ◽  
Xiaojuan Lou ◽  
Qiang Dong
Keyword(s):  
First Passage Time ◽  
Passage Time ◽  
Bistable System ◽  
Lévy Noise ◽  
Mean First Passage Time ◽  
First Passage ◽  
System Parameters ◽  
Text Response ◽  
The Mean ◽  
Levy Noise

In this paper, the first-passage behavior of under-damped asymmetric bistable system driven by Lévy noise is studied. The two aspects considered are the mean first-passage time (MFPT) and the distribution of first-passage time in two opposite directions. To begin with, using the Janicki–Weron algorithm to generate Lévy noise, the system driven by Lévy noise is simulated through the fourth-order Runge–Kutta algorithm. Then the first-passage time of [Formula: see text] response tracks is calculated, and the MFPT and the distribution of first-passage time are obtained. Finally, the influence of Lévy noise and system parameters on MFPT and the distribution of first-passage time are analyzed. Moreover, the noise enhanced stability (NES) effect is found.

scholarly journals Dynamics of Nonautonomous Stochastic Gilpin-Ayala Competition Model with Jumps

2013 ◽  
Vol 2013 ◽  
pp. 1-12 ◽  
Author(s):  
Yanchao Zang ◽  
Junping Li ◽  
Jiangang Liu
Keyword(s):  
Asymptotic Behavior ◽  
Positive Solution ◽  
Sufficient Conditions ◽  
Competition Model ◽  
Lévy Noise ◽  
Model Driven ◽  
Global Positive Solution ◽  
The Mean ◽  
Pathwise Estimation ◽  
Levy Noise

The nonautonomous stochastic Gilpin-Ayala competition model driven by Lévy noise is considered. First, it is shown that this model has a global positive solution. Then, we discuss the asymptotic behavior of the solution including moment and pathwise estimation. Finally, sufficient conditions for extinction, nonpersistence in the mean, and weak persistence of the solution are established.

Simply supported FPEDs connected by springs for broadband energy harvesting

2020 ◽  
Vol 64 (1-4) ◽  
pp. 201-210
Author(s):  
Yoshikazu Tanaka ◽  
Satoru Odake ◽  
Jun Miyake ◽  
Hidemi Mutsuda ◽  
Atanas A. Popov ◽  
...  
Keyword(s):  
Energy Harvesting ◽  
Evaluation Method ◽  
Energy Harvester ◽  
Vibrational Energy ◽  
Functional Materials ◽  
Vibration Energy ◽  
Theoretical Evaluation ◽  
Vibration Energy Harvester ◽  
Polyvinylidene Difluoride ◽  
Simply Supported

Energy harvesting methods that use functional materials have attracted interest because they can take advantage of an abundant but underutilized energy source. Most vibration energy harvester designs operate most effectively around their resonant frequency. However, in practice, the frequency band for ambient vibrational energy is typically broad. The development of technologies for broadband energy harvesting is therefore desirable. The authors previously proposed an energy harvester, called a flexible piezoelectric device (FPED), that consists of a piezoelectric film (polyvinylidene difluoride) and a soft material, such as silicon rubber or polyethylene terephthalate. The authors also proposed a system based on FPEDs for broadband energy harvesting. The system consisted of cantilevered FPEDs, with each FPED connected via a spring. Simply supported FPEDs also have potential for broadband energy harvesting, and here, a theoretical evaluation method is proposed for such a system. Experiments are conducted to validate the derived model.

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