scholarly journals Stochastic bifurcation in generalized chua's circuit through alpha-stable levy noise

2017 ◽  
Author(s):  
Ferit Acar Savaci ◽  
Serpil Yilmaz
Keyword(s):  
Lévy Noise ◽  
Stochastic Bifurcation ◽  
Chua’S Circuit ◽  
Chua's Circuit ◽  
Levy Noise

scholarly journals Stochastic bifurcation in single-species model induced by α-stable Lévy noise

2021 ◽  
Vol 2021 (10) ◽  
pp. 103403
Author(s):  
Almaz Tesfay ◽  
Daniel Tesfay ◽  
Shenglan Yuan ◽  
James Brannan ◽  
Jinqiao Duan
Keyword(s):  
Single Species ◽  
Lévy Noise ◽  
Stochastic Bifurcation ◽  
Levy Noise ◽  
Single Species Model

Stochastic bifurcation for a tumor–immune system with symmetric Lévy noise

2013 ◽  
Vol 392 (20) ◽  
pp. 4739-4748 ◽  
Author(s):  
Yong Xu ◽  
Jing Feng ◽  
JuanJuan Li ◽  
Huiqing Zhang
Keyword(s):  
Immune System ◽  
Lévy Noise ◽  
Stochastic Bifurcation ◽  
Levy Noise

Stochastic Bifurcation in Generalized Chua’s Circuit Driven by Skew-Normal Distributed Noise

2018 ◽  
Vol 17 (04) ◽  
pp. 1830002 ◽  
Author(s):  
Serpil Yilmaz ◽  
M. Emre Cek ◽  
F. Acar Savaci
Keyword(s):  
Noise Intensity ◽  
Piecewise Linear ◽  
Stochastic Bifurcation ◽  
Chua’S Circuit ◽  
Stationary Distributions ◽  
Chua's Circuit ◽  
Skewness Parameter ◽  
Skew Normal ◽  
Stochastic Responses

In this study, the stochastic phenomenological bifurcations (P-bifurcations) of generalized Chua’s circuit (GCC) driven by skew-normal distributed noise have been investigated by numerically obtaining the stationary distributions of the stochastic responses. The noise intensity and/or skewness parameters of skew-normal distributed noise have been chosen as the bifurcation parameters to change the structure of the stochastic attractor. While the number of breakpoints in the piecewise-linear characteristics of the GCC are fixed, it has been observed that the number of scrolls have been changed by tuning the noise intensity and the skewness parameter of the skew-normal distributed noise.

scholarly journals A Stochastic Pitchfork Bifurcation in Most Probable Phase Portraits

2018 ◽  
Vol 28 (01) ◽  
pp. 1850017 ◽  
Author(s):  
Hui Wang ◽  
Xiaoli Chen ◽  
Jinqiao Duan
Keyword(s):  
Gaussian Noise ◽  
Pitchfork Bifurcation ◽  
Phase Portraits ◽  
Lévy Noise ◽  
Stochastic Bifurcation ◽  
Bifurcation Phenomena ◽  
Pitchfork Bifurcations ◽  
Non Gaussian ◽  
Levy Noise ◽  
Qualitative Changes

We study stochastic bifurcation for a system under multiplicative stable Lévy noise (an important class of non-Gaussian noise), by examining the qualitative changes of equilibrium states with its most probable phase portraits. We have found some peculiar bifurcation phenomena in contrast to the deterministic counterpart: (i) When the non-Gaussianity parameter in Lévy noise varies, there is either one, two or no backward pitchfork type bifurcations; (ii) When a parameter in the vector field varies, there are two or three forward pitchfork bifurcations; (iii) The non-Gaussian Lévy noise clearly leads to fundamentally more complex bifurcation scenarios, since in the special case of Gaussian noise, there is only one pitchfork bifurcation which is reminiscent of the deterministic situation.

scholarly journals An Enhanced Intrinsic Time-Scale Decomposition Method Based on Adaptive Lévy Noise and Its Application in Bearing Fault Diagnosis

Symmetry ◽  
2021 ◽  
Vol 13 (4) ◽  
pp. 617
Author(s):  
Jianpeng Ma ◽  
Shi Zhuo ◽  
Chengwei Li ◽  
Liwei Zhan ◽  
Guangzhu Zhang
Keyword(s):  
Fault Diagnosis ◽  
Time Scale ◽  
Lévy Noise ◽  
Model Parameters ◽  
Rolling Bearings ◽  
Intrinsic Time ◽  
Time Scale Decomposition ◽  
Weak Fault ◽  
Levy Noise ◽  
The Impact

When early failures in rolling bearings occur, we need to be able to extract weak fault characteristic frequencies under the influence of strong noise and then perform fault diagnosis. Therefore, a new method is proposed: complete ensemble intrinsic time-scale decomposition with adaptive Lévy noise (CEITDALN). This method solves the problem of the traditional complete ensemble intrinsic time-scale decomposition with adaptive noise (CEITDAN) method not being able to filter nonwhite noise in measured vibration signal noise. Therefore, in the method proposed in this paper, a noise model in the form of parameter-adjusted noise is used to replace traditional white noise. We used an optimization algorithm to adaptively adjust the model parameters, reducing the impact of nonwhite noise on the feature frequency extraction. The experimental results for the simulation and vibration signals of rolling bearings showed that the CEITDALN method could extract weak fault features more effectively than traditional methods.

Sign in / Sign up

Export Citation Format

Share Document