Stochastic D-bifurcation for a damped sine-Gordon equation with noise

Stochastic D-bifurcation for a damped sine-Gordon equation with noise

We investigate the stochastic bifurcation of a damped sine-Gordon equation with Dirichlet boundary conditions under the influence of multiplicative Gaussian white noise. Introducing a slow time scale, we derive the amplitude equations near the trivial solution by multiscale analysis. And the station...

Full description

Bibliographic Details
Main Authors: Qiongwei Huang, Changfeng Xue, Jiashi Tang
Format: Article
Language:English
Published: AIP Publishing LLC 2015-04-01
Series:AIP Advances
Online Access:http://dx.doi.org/10.1063/1.4918302
id doaj-ee90889598c749d2ae0f03ff761a3d04
record_format Article
spelling doaj-ee90889598c749d2ae0f03ff761a3d042020-11-24T23:39:30ZengAIP Publishing LLCAIP Advances2158-32262015-04-0154047121047121-610.1063/1.4918302021504ADVStochastic D-bifurcation for a damped sine-Gordon equation with noiseQiongwei Huang0Changfeng Xue1Jiashi Tang2Department of Fundamental Sciences, Yancheng Institute of Technology, Yancheng 224051, PR ChinaDepartment of Fundamental Sciences, Yancheng Institute of Technology, Yancheng 224051, PR ChinaCollege of Mechanical and Vehicle Engineering, Hunan University, Changsha 410082, PR ChinaWe investigate the stochastic bifurcation of a damped sine-Gordon equation with Dirichlet boundary conditions under the influence of multiplicative Gaussian white noise. Introducing a slow time scale, we derive the amplitude equations near the trivial solution by multiscale analysis. And the stationary probability density functions are formulated analytically using the stochastic averaging of energy envelope. The numerical calculations show that the system undergoes a stochastic D-bifurcation of energy envelope from a delta measure to new stationary measures when the control parameter crosses a critical point.http://dx.doi.org/10.1063/1.4918302
collection DOAJ
language English
format Article
sources DOAJ
author Qiongwei Huang
Changfeng Xue
Jiashi Tang
spellingShingle Qiongwei Huang
Changfeng Xue
Jiashi Tang
Stochastic D-bifurcation for a damped sine-Gordon equation with noise
AIP Advances
author_facet Qiongwei Huang
Changfeng Xue
Jiashi Tang
author_sort Qiongwei Huang
title Stochastic D-bifurcation for a damped sine-Gordon equation with noise
title_short Stochastic D-bifurcation for a damped sine-Gordon equation with noise
title_full Stochastic D-bifurcation for a damped sine-Gordon equation with noise
title_fullStr Stochastic D-bifurcation for a damped sine-Gordon equation with noise
title_full_unstemmed Stochastic D-bifurcation for a damped sine-Gordon equation with noise
title_sort stochastic d-bifurcation for a damped sine-gordon equation with noise
publisher AIP Publishing LLC
series AIP Advances
issn 2158-3226
publishDate 2015-04-01
description We investigate the stochastic bifurcation of a damped sine-Gordon equation with Dirichlet boundary conditions under the influence of multiplicative Gaussian white noise. Introducing a slow time scale, we derive the amplitude equations near the trivial solution by multiscale analysis. And the stationary probability density functions are formulated analytically using the stochastic averaging of energy envelope. The numerical calculations show that the system undergoes a stochastic D-bifurcation of energy envelope from a delta measure to new stationary measures when the control parameter crosses a critical point.
url http://dx.doi.org/10.1063/1.4918302
work_keys_str_mv AT qiongweihuang stochasticdbifurcationforadampedsinegordonequationwithnoise
AT changfengxue stochasticdbifurcationforadampedsinegordonequationwithnoise
AT jiashitang stochasticdbifurcationforadampedsinegordonequationwithnoise
_version_ 1725513163648008192

Similar Items