Application of Complex Fractional Moment in nonlinear system with Gaussian colored noise

Lizhi Niu; Yi Song; Wei Xu

doi:10.1016/j.ijnonlinmec.2022.103945

Application of Complex Fractional Moment in nonlinear system with Gaussian colored noise

Lizhi Niu, Yi Song, Wei Xu

School of Mathematics and Statistics

Northwestern Polytechnical University Xian

Research output: Contribution to journal › Article › peer-review

9 Scopus citations

Abstract

This paper studies the transient response of the nonlinear system with Gaussian colored noise. The one-dimensional Itô stochastic differential equation with respect to amplitude response is obtained by the stochastic averaging technique, and the Mellin transformation is applied to the related Fokker–Planck–Kolmogorov (FPK) equation to obtain a set of Complex Fractional Moment (CFM) differential equations. The semi-analytical solution of the FPK equation can be reconstructed by solving the CFM equations. Numerical method is adopted to verify the validity of the CFM method, and the dynamical temporal behaviors of the transient response Probability Density Function (PDF) are analyzed. In addition, the transient bifurcation phenomenon of the system is discussed, and the 3-D distribution diagram of peak value of transient PDF is produced.

Original language	English
Article number	103945
Journal	International Journal of Non-Linear Mechanics
Volume	141
DOIs	https://doi.org/10.1016/j.ijnonlinmec.2022.103945
State	Published - May 2022

Keywords

Bifurcation
Complex fractional moment
Gaussian colored noise
Nonlinear dynamics
Transient response

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10.1016/j.ijnonlinmec.2022.103945

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@article{5580cf1498904ff3a710fb9ddc0c72a8,

title = "Application of Complex Fractional Moment in nonlinear system with Gaussian colored noise",

abstract = "This paper studies the transient response of the nonlinear system with Gaussian colored noise. The one-dimensional It{\^o} stochastic differential equation with respect to amplitude response is obtained by the stochastic averaging technique, and the Mellin transformation is applied to the related Fokker–Planck–Kolmogorov (FPK) equation to obtain a set of Complex Fractional Moment (CFM) differential equations. The semi-analytical solution of the FPK equation can be reconstructed by solving the CFM equations. Numerical method is adopted to verify the validity of the CFM method, and the dynamical temporal behaviors of the transient response Probability Density Function (PDF) are analyzed. In addition, the transient bifurcation phenomenon of the system is discussed, and the 3-D distribution diagram of peak value of transient PDF is produced.",

keywords = "Bifurcation, Complex fractional moment, Gaussian colored noise, Nonlinear dynamics, Transient response",

author = "Lizhi Niu and Yi Song and Wei Xu",

note = "Publisher Copyright: {\textcopyright} 2022 Elsevier Ltd",

year = "2022",

month = may,

doi = "10.1016/j.ijnonlinmec.2022.103945",

language = "英语",

volume = "141",

journal = "International Journal of Non-Linear Mechanics",

issn = "0020-7462",

publisher = "Elsevier Ltd",

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TY - JOUR

T1 - Application of Complex Fractional Moment in nonlinear system with Gaussian colored noise

AU - Niu, Lizhi

AU - Song, Yi

AU - Xu, Wei

PY - 2022/5

Y1 - 2022/5

N2 - This paper studies the transient response of the nonlinear system with Gaussian colored noise. The one-dimensional Itô stochastic differential equation with respect to amplitude response is obtained by the stochastic averaging technique, and the Mellin transformation is applied to the related Fokker–Planck–Kolmogorov (FPK) equation to obtain a set of Complex Fractional Moment (CFM) differential equations. The semi-analytical solution of the FPK equation can be reconstructed by solving the CFM equations. Numerical method is adopted to verify the validity of the CFM method, and the dynamical temporal behaviors of the transient response Probability Density Function (PDF) are analyzed. In addition, the transient bifurcation phenomenon of the system is discussed, and the 3-D distribution diagram of peak value of transient PDF is produced.

AB - This paper studies the transient response of the nonlinear system with Gaussian colored noise. The one-dimensional Itô stochastic differential equation with respect to amplitude response is obtained by the stochastic averaging technique, and the Mellin transformation is applied to the related Fokker–Planck–Kolmogorov (FPK) equation to obtain a set of Complex Fractional Moment (CFM) differential equations. The semi-analytical solution of the FPK equation can be reconstructed by solving the CFM equations. Numerical method is adopted to verify the validity of the CFM method, and the dynamical temporal behaviors of the transient response Probability Density Function (PDF) are analyzed. In addition, the transient bifurcation phenomenon of the system is discussed, and the 3-D distribution diagram of peak value of transient PDF is produced.

KW - Bifurcation

KW - Complex fractional moment

KW - Gaussian colored noise

KW - Nonlinear dynamics

KW - Transient response

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U2 - 10.1016/j.ijnonlinmec.2022.103945

DO - 10.1016/j.ijnonlinmec.2022.103945

M3 - 文章

AN - SCOPUS:85124608580

SN - 0020-7462

VL - 141

JO - International Journal of Non-Linear Mechanics

JF - International Journal of Non-Linear Mechanics

M1 - 103945

ER -

Application of Complex Fractional Moment in nonlinear system with Gaussian colored noise

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Keywords

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