Stochastic stability of variable-mass Duffing oscillator with mass disturbance modeled as Gaussian white noise

2017 ◽  
Vol 89 (1) ◽  
pp. 607-616 ◽  
Author(s):  
Yan Qiao ◽  
Wei Xu ◽  
Wantao Jia ◽  
Weiyan Liu
Keyword(s):  
White Noise ◽  
Stochastic Stability ◽  
Duffing Oscillator ◽  
Gaussian White Noise ◽  
Variable Mass

Extension of Nonlinear Stochastic Solution to Include Sinusoidal Excitation—Illustrated by Duffing Oscillator

2017 ◽  
Vol 12 (5) ◽  
Author(s):  
R. J. Chang
Keyword(s):  
White Noise ◽  
Correction Factor ◽  
Duffing Oscillator ◽  
Gaussian White Noise ◽  
Noise Spectrum ◽  
Linearization Method ◽  
Algebraic Equations ◽  
Stochastic Solution ◽  
Non Gaussian ◽  
Sinusoidal Excitation

A new non-Gaussian linearization method is developed for extending the analysis of Gaussian white-noise excited nonlinear oscillator to incorporate sinusoidal excitation. The non-Gaussian linearization method is developed through introducing a modulated correction factor on the linearization coefficient which is obtained by Gaussian linearization. The time average of cyclostationary response of variance and noise spectrum is analyzed through the correction factor. The validity of the present non-Gaussian approach in predicting the statistical response is supported by utilizing Monte Carlo simulations. The present non-Gaussian analysis, without imposing restrictive analytical conditions, can be obtained by solving nonlinear algebraic equations. The non-Gaussian solution effectively predicts accurate sinusoidal and noise response when the nonlinear system is subjected to both sinusoidal and white-noise excitations.

scholarly journals The Stochastic Stability of Internal HIV Models with Gaussian White Noise and Gaussian Colored Noise

2019 ◽  
Vol 2019 ◽  
pp. 1-8 ◽  
Author(s):  
Xiying Wang ◽  
Yuanxiao Li ◽  
Xiaomei Wang
Keyword(s):  
White Noise ◽  
Probability Density ◽  
Stochastic Stability ◽  
Colored Noise ◽  
Gaussian White Noise ◽  
Probability Density Functions ◽  
Stochastic Dynamic ◽  
Density Functions ◽  
Gaussian Colored Noise ◽  
The Stability

In this paper, the stochastic stability of internal HIV models driven by Gaussian white noise and Gaussian colored noise is analyzed. First, the stability of deterministic models is investigated. By analyzing the characteristic values of endemic equilibrium, we could obtain that internal HIV models reach a steady state under the influence of RTI and PI drugs. Then we discuss the stochastic stability of internal HIV models driven by Gaussian white noise and Gaussian colored noise, based on probability density functions. The functional methods are carried out to derive the approximate Fokker-Planck equation of stochastic internal HIV systems and further obtain the marginal probability density functions. Finally, numerical results show that the noise intensities have a great influence on uninfected cell, infected cell, and virus particles, for predicting the stability of stochastic dynamic systems subjected to Gaussian white noise and Gaussian colored noise.

Probabilistic Solution of Vibro-Impact Systems Under Additive Gaussian White Noise

2014 ◽  
Vol 136 (3) ◽  
Author(s):  
H. T. Zhu
Keyword(s):  
White Noise ◽  
Duffing Oscillator ◽  
Gaussian White Noise ◽  
Planck Equation ◽  
Solution Procedure ◽  
Additive Gaussian White Noise ◽  
Stationary Probability Density Function ◽  
Probabilistic Solution ◽  
Zero Offset ◽  
Polynomial Closure

This paper presents a solution procedure for the stationary probability density function (PDF) of the response of vibro-impact systems under additive Gaussian white noise. The constraint is a unilateral zero-offset barrier. The vibro-impact system is first converted into a system without barriers using the Zhuravlev nonsmooth coordinate transformation. The stationary PDF of the converted system is governed by the Fokker–Planck equation which is solved by the exponential-polynomial closure (EPC) method. A vibro-impact Duffing oscillator with either elastic or lightly inelastic impacts is considered in a numerical analysis. Meanwhile, the level of nonlinearity in displacement is also examined in this study as well as the case of negative linear stiffness. Comparison with the simulated results shows that the EPC method can present a satisfactory PDF for displacement and velocity when the polynomial order is taken as 4 in the investigated cases. The tail of the PDF also works well with the simulated result.

Stationary Solution of Duffing Oscillator Driven by Additive and Multiplicative Colored Noise Excitations

2017 ◽  
Vol 139 (2) ◽  
Author(s):  
Siu-Siu Guo ◽  
Qingxuan Shi
Keyword(s):  
White Noise ◽  
Colored Noise ◽  
Duffing Oscillator ◽  
Gaussian White Noise ◽  
Approximate Solutions ◽  
Intensity Level ◽  
First Order ◽  
Fpk Equation ◽  
Polynomial Closure ◽  
Mcs Method

A bistable Duffing oscillator subjected to additive and multiplicative Ornstein–Uhlenbeck (OU) colored excitations is examined. It is modeled through a set of four first-order stochastic differential equations by representing the OU excitations as filtered Gaussian white noise excitations. Enlargement in the state-space vector leads to four-dimensional (4D) Fokker–Planck–Kolmogorov (FPK) equation. The exponential-polynomial closure (EPC) method, proposed previously for the case of white noise excitations, is further improved and developed to solve colored noise case, resulting in much more polynomial terms included in the approximate solution. Numerical results show that approximate solutions from the EPC method compare well with the predictions obtained via Monte Carlo simulation (MCS) method. Investigation is also carried out to examine the influence of intensity level on the probability distribution solutions of system responses.

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